Publikationen

Monografien

  • U. Wilbrandt, Stokes--Darcy Equations Analytic and Numerical Analysis, D. Bresch, V. John, M. Hieber, I. Kukavica, J. Robinson, Y. Shibata, eds., Advances in Mathematical Fluid Mechanics, Lecture Notes in Mathematical Fluid Mechanics, Springer Nature Switzerland AG (Birkhäuser), 2019, pp. i-viii, 1--211, (Monograph Published), DOI 10.1007/978-3-030-02904-3 .

  • V.A. Garanzha, L. Kamenski, H. Si, eds., Numerical Geometry, Grid Generation and Scientific Computing. Proceedings of the 9th International Conference, NUMGRID 2018 / Voronoi 150, Celebrating the 150th Anniversary of G.F. Voronoi, Moscow, Russia, December 2018, 131 of Lecture Notes in Computational Science and Engineering, Springer Nature Switzerland AG, Cham, 2019, (Collection Published), DOI 10.1007/978-3-030-23436-2 .

  • A. Caiazzo, I.E. Vignon-Clementel, Chapter 3: Mathematical Modeling of Blood Flow in the Cardiovascular System, in: Quantification of Biophysical Parameters in Medical Imaging, I. Sack, T. Schaeffter, eds., Springer International Publishing, Cham, 2018, pp. 45--70, (Chapter Published), DOI 10.1007/978-3-319-65924-4_3 .

Artikel in Referierten Journalen

  • N. Alia, M. Pylvänäinen, V.-V. Visuri, V. John, S. Ollila, Vibrations of a laboratory-scale gas-stirred ladle with two eccentric nozzles and multiple sensors, Journal of Iron and Steel Research, International, 26 (2019), pp. 1031--1040, DOI 10.1007/s42243-019-00241-x .

  • A. Stephan, H. Stephan, Memory equations as reduced Markov processes, Discrete and Continuous Dynamical Systems, 39 (2019), pp. 2133--2155, DOI 10.3934/dcds.2019089 .
    Abstract
    A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with such a memory equation, we give an explicit construction of the corresponding Markov process. From a physical point of view the Markov process can be understood as the change of the type of some quasiparticles along one-way loops. Typically, the arising Markov process does not have the detailed balance property. The method leads to a more realisitc modeling of memory equations. Moreover, it carries over the large number of investigation tools for Markov processes to memory equations, like the calculation of the equilibrium state, the asymptotic behavior and so on. The method can be used for an approximative solution of some degenerate memory equations like delay differential equations.

  • P. Vágner, C. Guhlke, V. Miloš, R. Müller, J. Fuhrmann, A continuum model for yttria-stabilised zirconia incorporating triple phase boundary, lattice structure and immobile oxide ions, Journal of Solid State Electrochemistry, 23 (2019), pp. 2907--2926, DOI 10.1007/s10008-019-04356-9 .
    Abstract
    A continuum model for yttria-stabilised zirconia (YSZ) in the framework of non-equilibrium thermodynamics is developed. Particular attention is given to i) modeling of the YSZ-metal-gas triple phase boundary, ii) incorporation of the lattice structure and immobile oxide ions within the free energy model and iii) surface reactions. A finite volume discretization method based on modified Scharfetter-Gummel fluxes is derived in order to perform numerical simulations.
    The model is used to study the impact of yttria and immobile oxide ions on the structure of the charged boundary layer and the double layer capacitance. Cyclic voltammograms of an air-half cell are simulated to study the effect of parameter variations on surface reactions, adsorption and anion diffusion.

  • A. Zeghuzi, H.-J. Wünsche, H. Wenzel, M. Radziunas, J. Fuhrmann, A. Klehr, U. Bandelow, A. Knigge, Time-dependent simulation of thermal lensing in high-power broad-area semiconductor lasers, IEEE J. Select. Topics Quantum Electron., 25 (2019), 1502310, DOI 10.1109/JSTQE.2019.2925926 .

  • C. Bartsch, V. Wiedmeyer, Z. Lakdawala, R.I.A. Patterson, A. Voigt, K. Sundmacher, V. John, Stochastic-deterministic population balance modeling and simulation of a fluidized bed crystallizer experiment, Chemical Engineering Sciences, 208 (2019), 115102, DOI 10.1016/j.ces.2019.07.020 .

  • N.R. Gauger, A. Linke, P. Schroeder, On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond, SMAI Journal of Computational Mathematics, 5 (2019), pp. 89--129.
    Abstract
    Recently, high-order space discretisations were proposed for the numerical simulation of the incompressible Navier--Stokes equations at high Reynolds numbers, even for complicated domains from simulation practice. Although the overall spatial approximation order of the algorithms depends on the approximation quality of the boundary (often not better than third order), competitively accurate and efficient results were reported. In this contribution, first, a possible explanation for this somewhat surprising result is proposed: the velocity error of high-order space discretisations is more robust against quantitatively large and complicated pressure fields than low-order methods. Second, it is demonstrated that novel pressure-robust methods are significantly more accurate than comparable classical, non-pressure-robust space discretisations, whenever the quadratic, nonlinear convection term is a nontrivial gradient field like in certain generalised Beltrami flows at high Reynolds number. Then, pressure-robust methods even allow to halve the (formal) approximation order without compromising the accuracy. Third, classical high-order space discretisations are outperformed by pressure-robust methods whenever the boundary is not approximated with high-order accuracy. This improved accuracy of (low-order) pressure-robust mixed methods is explained in terms of a Helmholtz--Hodge projector, which cancels out the nonlinear convection term in any generalised Beltrami flow, since it is a gradient field. The numerical results are illustrated by a novel numerical analysis for pressure-robust and classical space discretisations. Further, the relevance of these results is discussed for flows that are not of Beltrami type.

  • A. Jha, V. John, A study of solvers for nonlinear AFC discretizations of convection-diffusion equations, Computational & Applied Mathematics, 78 (2019), DOI 10.1016/j.camwa.2019.04.020 .

  • V. Klika , M. Pavelka , P. Vágner, M. Grmela, Dynamic maximum entropy reduction, Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies, 21 (2019), pp. 1--27.

  • P.W. Schroeder, V. John, P.L. Lederer, Ch. Lehrenfeld, G. Lube, J. Schöberl, On reference solutions and the sensitivity of the 2D Kelvin--Helmholtz instability problem, Computers & Mathematics with Applications. An International Journal, 77 (2019), pp. 1010--1028.

  • J. DE Frutos, B. Garc'ia-Archilla, V. John, J. Novo, Error analysis of non inf-sup stable discretizations of the time-dependent Navier--Stokes equations with local projection stabilization, IMA Journal of Numerical Analysis, 39 (2019), pp. 1747--1786, DOI 10.1093/imanum/dry044 .

  • C. Bartsch, V. John, R.I.A. Patterson, Simulations of an ASA flow crystallizer with a coupled stochastic-deterministic approach, Comput. Chem. Engng., 124 (2019), pp. 350--363, DOI 10.1016/j.compchemeng.2019.01.012 .
    Abstract
    A coupled solver for population balance systems is presented, where the flow, temperature, and concentration equations are solved with finite element methods, and the particle size distribution is simulated with a stochastic simulation algorithm, a so-called kinetic Monte-Carlo method. This novel approach is applied for the simulation of an axisymmetric model of a tubular flow crystallizer. The numerical results are compared with experimental data.

  • W. Dreyer, C. Guhlke, R. Müller, The impact of solvation and dissociation on the transport parameters of liquid electrolytes: Continuum modeling and numerical study, European Physical Journal Special Topics, 227 (2019), pp. 2515--2538, DOI 10.1140/epjst/e2019-800133-2 .
    Abstract
    Electro-thermodynamics provides a consistent framework to derive continuum models for electrochemical systems. For the application to a specific experimental system, the general model must be equipped with two additional ingredients: a free energy model to calculate the chemical potentials and a kinetic model for the kinetic coefficients. Suitable free energy models for liquid electrolytes incorporating ion-solvent interaction, finite ion sizes and solvation already exist and have been validated against experimental measurements. In this work, we focus on the modeling of the mobility coefficients based on Maxwell--Stefan setting and incorporate them into the general electro-thermodynamic framework. Moreover, we discuss the impact of model parameter on conductivity, transference numbers and salt diffusion coefficient. In particular, the focus is set on the solvation of ions and incomplete dissociation of a non-dilute electrolyte.

  • P. Farrell, D. Peschka, Challenges for drift-diffusion simulations of semiconductors: A comparative study of different discretization philosophies, Computers & Mathematics with Applications. An International Journal, published online on 18.06.2019, DOI 10.1016/j.camwa.2019.06.007 .
    Abstract
    We analyze and benchmark the error and the convergence order of finite difference, finite-element as well as Voronoi finite-volume discretization schemes for the drift-diffusion equations describing charge transport in bulk semiconductor devices. Three common challenges, that can corrupt the precision of numerical solutions, will be discussed: boundary layers at Ohmic contacts, discontinuties in the doping profile, and corner singularities in L-shaped domains. The influence on the order of convergence is assessed for each computational challenge and the different discretization schemes. Additionally, we provide an analysis of the inner boundary layer asymptotics near Ohmic contacts to support our observations.

  • J. Fuhrmann, C. Guhlke, Ch. Merdon, A. Linke, R. Müller, Induced charge electroosmotic flow with finite ion size and solvation effects, Electrochimica Acta, 317 (2019), pp. 778--785, DOI 10.1016/j.electacta.2019.05.051 .

  • A. Linke, L.G. Rebholz, Pressure-induced locking in mixed methods for time-dependent (Navier--)Stokes equations, Journal of Computational Physics, 388 (2019), pp. 350--356, DOI 10.1016/j.jcp.2019.03.010 .
    Abstract
    We consider inf-sup stable mixed methods for the time-dependent incompressible Stokes and Navier--Stokes equations, extending earlier work on the steady (Navier-)Stokes Problem. A locking phenomenon is identified for classical inf-sup stable methods like the Taylor-Hood or the Crouzeix-Raviart elements by a novel, elegant and simple numerical analysis and corresponding numerical experiments, whenever the momentum balance is dominated by forces of a gradient type. More precisely, a reduction of the L2 convergence order for high order methods, and even a complete stall of the L2 convergence order for lowest-order methods on preasymptotic meshes is predicted by the analysis and practically observed. On the other hand, it is also shown that (structure-preserving) pressure-robust mixed methods do not suffer from this locking phenomenon, even if they are of lowest-order. A connection to well-balanced schemes for (vectorial) hyperbolic conservation laws like the shallow water or the compressible Euler equations is made.

  • M. Radziunas, J. Fuhrmann, A. Zeghuzi, H.-J. Wünsche, Th. Koprucki, C. Brée, H. Wenzel, U. Bandelow, Efficient coupling of electro-optical and heat-transport models for high-power broad-area semiconductor lasers, Optical and Quantum Electronics, 51 (2019), published online on 22.02.2019, DOI 10.1007/s11082-019-1792-1 .
    Abstract
    In this work, we discuss the modeling of edge-emitting high-power broad-area semiconductor lasers. We demonstrate an efficient iterative coupling of a slow heat transport (HT) model defined on multiple vertical-lateral laser cross-sections with a fast dynamic electro-optical (EO) model determined on the longitudinal-lateral domain that is a projection of the device to the active region of the laser. Whereas the HT-solver calculates temperature and thermally-induced refractive index changes, the EO-solver exploits these distributions and provides time-averaged field intensities, quasi-Fermi potentials, and carrier densities. All these time-averaged distributions are used repetitively by the HT-solver for the generation of the heat sources entering the HT problem solved in the next iteration step.

  • N. Alia, V. John, S. Ollila, Re-visiting the single-phase flow model for liquid steel ladle stirred by gas, Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems. Elsevier Science Inc., New York, NY. English, English abstracts., 67 (2019), pp. 549--556 (published online on 21.11.2018), DOI 10.1016/j.apm.2018.11.005 .

  • W. Dreyer, P. Friz, P. Gajewski, C. Guhlke, M. Maurelli, Stochastic many-particle model for LFP electrodes, Continuum Mechanics and Thermodynamics, 30 (2018), pp. 593--628, DOI 10.1007/s00161-018-0629-7 .
    Abstract
    In the framework of non-equilibrium thermodynamics we derive a new model for porous electrodes. The model is applied to LiFePO4 (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by surface fluctuations leading to a system of stochastic differential equations. The model is capable to derive an explicit relation between battery voltage and current that is controlled by thermodynamic state variables. This voltage-current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltagecharge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates.

  • M. Akbas, A. Linke, L.G. Rebholz, P.W. Schroeder, The analogue of grad-div stabilization in DG methods for incompressible flows: Limiting behavior and extension to tensor-product meshes, Computer Methods in Applied Mechanics and Engineering, 341 (2018), pp. 917--938, DOI 10.1016/j.cma.2018.07.019 .
    Abstract
    Grad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, for mitigating velocity errors that are sometimes called poor mass conservation. Such errors arise due to the relaxation of the divergence constraint in classical mixed methods, and are excited whenever the spacial discretization has to deal with comparably large and complicated pressures. In this contribution, an analogue of grad-div stabilization is presented for nonconforming flow discretizations of Discontinuous Galerkin or nonconforming finite element type. Here the key is the penalization of the jumps of the normal velocities over facets of the triangulation, which controls the measure-valued part of the distributional divergence of the discrete velocity solution. Furthermore, we characterize the limit for arbitrarily large penalization parameters, which shows that the proposed nonconforming Discontinuous Galerkin methods remain robust and accurate in this limit. Several numerical examples illustrate the theory and show their relevance for the simulation of practical, nontrivial flows.

  • G.R. Barrenechea, V. John, P. Knobloch, R. Rankin, A unified analysis of algebraic flux correction schemes for convection-diffusion equations, SeMA Journal. Boletin de la Sociedad Espannola de Matematica Aplicada, 75 (2018), pp. 655--685, DOI 10.1007/s40324-018-0160-6 .

  • A. Bradji, J. Fuhrmann, On the convergence and convergence order of finite volume gradient schemes for oblique derivative boundary value problems, Computational & Applied Mathematics, 37 (2018), pp. 2533--2565, DOI 10.1007/s40314-017-0463-8 .

  • A. Horn, A. Li, T.A. Dembek, A. Kappel, C. Boulay, H. Si, ET AL., Lead-DBS v2: Towards a comprehensive pipeline for deep brain stimulation imaging, NeuroImage, 1 (2018), pp. 293--316, DOI 10.1016/j.neuroimage.2018.08.068 .

  • M. Patriarca, P. Farrell, J. Fuhrmann, Th. Koprucki, Highly accurate quadrature-based Scharfetter--Gummel schemes for charge transport in degenerate semiconductors, Computer Physics Communications. An International Journal and Program Library for Computational Physics and Physical Chemistry, 235 (2019), pp. 40--49 (published online on 16.10.2018), DOI 10.1016/j.cpc.2018.10.004 .
    Abstract
    We introduce a family of two point flux expressions for charge carrier transport described by drift-diffusion problems in degenerate semiconductors with non-Boltzmann statistics which can be used in Voronoï finite volume discretizations. In the case of Boltzmann statistics, Scharfetter and Gummel derived such fluxes by solving a linear two point boundary value problem yielding a closed form expression for the flux. Instead, a generalization of this approach to the nonlinear case yields a flux value given implicitly as the solution of a nonlinear integral equation. We examine the solution of this integral equation numerically via quadrature rules to approximate the integral as well as Newton's method to solve the resulting approximate integral equation. This approach results into a family of quadrature-based Scharfetter-Gummel flux approximations. We focus on four quadrature rules and compare the resulting schemes with respect to execution time and accuracy. A convergence study reveals that the solution of the approximate integral equation converges exponentially in terms of the number of quadrature points. With very few integration nodes they are already more accurate than a state-of-the-art reference flux, especially in the challenging physical scenario of high nonlinear diffusion. Finally, we show that thermodynamic consistency is practically guaranteed.

  • P.W. Schroeder, Ch. Lehrenfeld, A. Linke, G. Lube, Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier--Stokes equations, SeMA Journal. Boletin de la Sociedad Espannola de Matematica Aplicada, 75 (2018), pp. 629--653, DOI 10.1007/s40324-018-0157-1 .
    Abstract
    Inf-sup stable FEM applied to time-dependent incompressible Navier--Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure-robustness ensures the fulfilment of a fundamental invariance principle and velocity error estimates are not corrupted by the pressure approximability. Secondly, Re-semi-robustness means that constants appearing on the right-hand side of kinetic and dissipation energy error estimates (including Gronwall constants) do not explicitly depend on the Reynolds number. Such estimates rely on an essential regularity assumption for the gradient of the velocity, which is discussed in detail. In the sense of best practice, we review and establish pressure- and Re-semi-robust estimates for pointwise divergence-free H1-conforming FEM (like Scott--Vogelius pairs or certain isogeometric based FEM) and pointwise divergence-free H(div)-conforming discontinuous Galerkin FEM. For convection-dominated problems, the latter naturally includes an upwind stabilisation for the velocity which is not gradient-based.

  • J. DE Frutos, B. Garc'ia-Archilla, V. John, J. Novo, Analysis of the grad-div stabilization for the time-dependent Navier--Stokes equations with inf-sup stable finite elements, Advances in Computational Mathematics, 44 (2018), pp. 195--225.

  • L. Blank, A. Caiazzo, F. Chouly, A. Lozinski, J. Mura, Analysis of a stabilized penalty-free Nitsche method for the Brinkman, Stokes, and Darcy problems, ESAIM: Mathematical Modelling and Numerical Analysis, 52 (2018), pp. 2149--2185, DOI 10.1051/m2an/2018063 .

  • N. Ahmed, C. Bartsch, V. John, U. Wilbrandt, An assessment of solvers for some saddle point problems emerging from the incompressible Navier--Stokes equations, Computer Methods in Applied Mechanics and Engineering, 331 (2018), pp. 492--513, DOI 10.1016/j.cma.2017.12.004 .
    Abstract
    Efficient incompressible flow simulations, using inf-sup stable pairs of finite element spaces, require the application of efficient solvers for the arising linear saddle point problems. This paper presents an assessment of different solvers: the sparse direct solver UMFPACK, the flexible GMRES (FGMRES) method with different coupled multigrid preconditioners, and FGMRES with Least Squares Commutator (LSC) preconditioners. The assessment is performed for steady-state and time-dependent flows around cylinders in 2d and 3d. Several pairs of inf-sup stable finite element spaces with second order velocity and first order pressure are used. It turns out that for the steady-state problems often FGMRES with an appropriate multigrid preconditioner was the most efficient method on finer grids. For the time-dependent problems, FGMRES with LSC preconditioners that use an inexact iterative solution of the velocity subproblem worked best for smaller time steps.

  • N. Ahmed, V. John, G. Matthies, J. Novo, A local projection stabilization/continuous Galerkin--Petrov method for incompressible flow problems, Applied Mathematics and Computation, 333 (2018), pp. 304--324, DOI 10.1016/j.amc.2018.03.088 .
    Abstract
    The local projection stabilization (LPS) method in space is consid-ered to approximate the evolutionary Oseen equations. Optimal error bounds independent of the viscosity parameter are obtained in the continuous-in-time case for the approximations of both velocity and pressure. In addition, the fully discrete case in combination with higher order continuous Galerkin--Petrov (cGP) methods is studied. Error estimates of order k + 1 are proved, where k denotes the polynomial degree in time, assuming that the convective term is time-independent. Numerical results show that the predicted order is also achieved in the general case of time-dependent convective terms.

  • N. Ahmed, A. Linke, Ch. Merdon, On really locking-free mixed finite element methods for the transient incompressible Stokes equations, SIAM Journal on Numerical Analysis, 56 (2018), pp. 185--209.
    Abstract
    Inf-sup stable mixed methods for the steady incompressible Stokes equations that relax the divergence constraint are often claimed to deliver locking-free discretizations. However, this relaxation leads to a pressure-dependent contribution in the velocity error, which is proportional to the inverse of the viscosity, thus giving rise to a (different) locking phenomenon. However, a recently proposed modification of the right hand side alone leads to a discretization that is really locking-free, i.e., its velocity error converges with optimal order and is independent of the pressure and the smallness of the viscosity. In this contribution, we extend this approach to the transient incompressible Stokes equations, where besides the right hand side also the velocity time derivative requires an improved space discretization. Semi-discrete and fully-discrete a-priori velocity and pressure error estimates are derived, which show beautiful robustness properties. Two numerical examples illustrate the superior accuracy of pressure-robust space discretizations in the case of small viscosities.

  • W. Dreyer, C. Guhlke, R. Müller, Bulk-surface electro-thermodynamics and applications to electrochemistry, Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies, 20 (2018), pp. 939/1--939/44, DOI 10.3390/e20120939 .
    Abstract
    We propose a modeling framework for magnetizable, polarizable, elastic, viscous, heat conducting, reactive mixtures in contact with interfaces. To this end we first introduce bulk and surface balance equations that contain several constitutive quantities. For further modeling the constitutive quantities, we formulate constitutive principles. They are based on an axiomatic introduction of the entropy principle and the postulation of Galilean symmetry. We apply the proposed formalism to derive constitutive relations in a rather abstract setting. For illustration of the developed procedure, we state an explicit isothermal material model for liquid electrolyte metal electrode interfaces in terms of free energy densities in the bulk and on the surface. Finally we give a survey of recent advancements in the understanding of electrochemical interfaces that were based on this model.

  • P. Farrell, M. Patriarca, J. Fuhrmann, Th. Koprucki, Comparison of thermodynamically consistent charge carrier flux discretizations for Fermi--Dirac and Gauss--Fermi statistics, Optical and Quantum Electronics, 50 (2018), pp. 101/1--101/10, DOI 10.1007/s11082-018-1349-8 .
    Abstract
    We compare three thermodynamically consistent Scharfetter--Gummel schemes for different distribution functions for the carrier densities, including the Fermi--Dirac integral of order 1/2 and the Gauss--Fermi integral. The most accurate (but unfortunately also most costly) generalized Scharfetter--Gummel scheme requires the solution of an integral equation. We propose a new method to solve this integral equation numerically based on Gauss quadrature and Newton's method. We discuss the quality of this approximation and plot the resulting currents for Fermi--Dirac and Gauss--Fermi statistics. Finally, by comparing two modified (diffusion-enhanced and inverse activity based) Scharfetter--Gummel schemes with the more accurate generalized scheme, we show that the diffusion-enhanced ansatz leads to considerably lower flux errors, confirming previous results (J. Comp. Phys. 346:497-513, 2017).

  • V. John, S. Kaya, J. Novo, Finite element error analysis of a mantle convection model, International Journal of Numerical Analysis and Modeling. Wuhan University, Wuhan and Institute for Scientific Computing and Information(ISCI), Edmonton, Alberta. English., 15 (2018), pp. 677--698, DOI 10.20347/WIAS.PREPRINT.2403 .
    Abstract
    A mantle convection model consisting of the stationary Stokes equations and a time-dependent convection-diffusion equation for the temperature is studied. The Stokes problem is discretized with a conforming inf-sup stable pair of finite element spaces and the temperature equation is stabilized with the SUPG method. Finite element error estimates are derived which show the dependency of the error of the solution of one problem on the error of the solution of the other equation. The dependency of the error bounds on the coefficients of the problem is monitored.

  • V. John, P. Knobloch, J. Novo, Finite elements for scalar convection-dominated equations and incompressible flow problems -- A never ending story?, Computing and Visualization in Science, 19 (2018), pp. 47--63.
    Abstract
    The contents of this paper is twofold. First, important recent results concerning finite element methods for convection-dominated problems and incompressible flow problems are described that illustrate the activities in these topics. Second, a number of, in our opinion, important problems in these fields are discussed.

  • A. Linke, Ch. Merdon, M. Neilan, F. Neumann, Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes problem, Mathematics of Computation, 87 (2018), pp. 1543--1566, DOI 10.1090/mcom/3344 .
    Abstract
    Nearly all classical inf-sup stable mixed finite element methods for the incompressible Stokes equations are not pressure-robust, i.e., the velocity error is dependent on the pressure. However, recent results show that pressure-robustness can be recovered by a non-standard discretization of the right hand side alone. This variational crime introduces a consistency error in the method which can be estimated in a straightforward manner provided that the exact velocity solution is sufficiently smooth. The purpose of this paper is to analyze the pressure-robust scheme with low regularity. The numerical analysis applies divergence-free H¹-conforming Stokes finite element methods as a theoretical tool. As an example, pressure-robust velocity and pressure a-priori error estimates will be presented for the (first order) nonconforming Crouzeix--Raviart element. A key feature in the analysis is the dependence of the errors on the Helmholtz projector of the right hand side data, and not on the entire data term. Numerical examples illustrate the theoretical results.

Beiträge zu Sammelwerken

  • N. Lei, W. Chen, Z. Luo, H. Si, X. Gu, Secondary power Diagram, dual of secondary polytope, in: Numerical Geometry, Grid Generation and Scientific Computing. Proceedings of the 9th International Conference, NUMGRID 2018 / Voronoi 150, V.A. Garanzha, L. Kamenski, H. Si, eds., 131 of Lecture Notes in Computational Science and Engineering, Springer Nature Switzerland AG, Cham, 2019, pp. 3--24, DOI 10.1007/978-3-030-23436-2 .

  • J. Fuhrmann, C. Guhlke, A. Linke, Ch. Merdon, R. Müller, Voronoi finite volumes and pressure robust finite elements for electrolyte models with finite ion sizes, in: Numerical Geometry, Grid Generation and Scientific Computing. Proceedings of the 9th International Conference, NUMGRID 2018 / Voronoi 150, V.A. Garanzha, L. Kamenski, H. Si, eds., 131 of Lecture Notes in Computational Science and Engineering, Springer Nature Switzerland AG, Cham, 2019, pp. 73--83, DOI 10.1007/978-3-030-23436-2 .

  • TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, On a database of simulated TEM images for In(Ga)As/GaAs quantum dots with various shapes, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2019), J. Piprek, K. Hinze, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2019, pp. 13--14 (appeared online 22.08.2019), DOI 10.1109/NUSOD.2019.8807025 .

  • A. Linke, Nonlinear flux approximation scheme for burgers equation derived from a local BVP, in: Numerical Mathematics and Advanced Applications 2017, Proceedings of ENUMATH 2017, F.A. Radu, K. Kumar, I. Berre, J.M. Nordbotten, I.S. Pop, eds., Springer, Berlin et al., 2019.

  • H. Si, A simple algorithm to triangulate a special class of 3D non-convex polyhedra without Steiner points, in: Numerical Geometry, Grid Generation and Scientific Computing. Proceedings of the 9th International Conference, NUMGRID 2018 / Voronoi 150, V.A. Garanzha, L. Kamenski, H. Si, eds., 131 of Lecture Notes in Computational Science and Engineering, Springer Nature Switzerland AG, Cham, 2019, pp. 61--71, DOI 10.1007/978-3-030-23436-2 .

  • M. Patriarca, P. Farrell, J. Fuhrmann, Th. Koprucki, M. Auf DER Maur, Highly accurate discretizations for non-Boltzmann charge transport in semiconductors, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2018, pp. 53--54.

  • TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Towards model-based geometry reconstruction of quantum dots from TEM, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2018, pp. 115--116.

  • M. Radziunas, J. Fuhrmann, A. Zeghuzi, H.-J. Wünsche, Th. Koprucki, H. Wenzel, U. Bandelow, Efficient coupling of heat flow and electro-optical models for simulation of dynamics in high-power broad-area semiconductor devices, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), J. Piprek, A.B. Djurisic, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2018, pp. 91--92.

Preprints, Reports, Technical Reports

  • M. Akbas, Th. Gallouët, A. Gassmann, A. Linke, Ch. Merdon, A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem, Preprint no. 2641, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2641 .
    Abstract, PDF (445 kByte)
    A novel notion for constructing a well-balanced scheme --- a gradient-robust scheme --- is introduced and a showcase application for a steady compressible, isothermal Stokes equations is presented. Gradient-robustness means that arbitrary gradient fields in the momentum balance are well-balanced by the discrete pressure gradient --- if there is enough mass in the system to compensate the force. The scheme is asymptotic-preserving in the sense that it degenerates for low Mach numbers to a recent inf-sup stable and pressure-robust discretization for the incompressible Stokes equations. The convergence of the coupled FEM-FVM scheme for the nonlinear, isothermal Stokes equations is proved by compactness arguments. Numerical examples illustrate the numerical analysis, and show that the novel approach can lead to a dramatically increased accuracy in nearly-hydrostatic low Mach number flows. Numerical examples also suggest that a straight-forward extension to barotropic situations with nonlinear equations of state is feasible.

  • J. Fuhrmann, M. Landstorfer, R. Müller, Modeling polycrystalline electrode-electrolyte interfaces: The differential capacitance, Preprint no. 2640, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2640 .
    Abstract, PDF (3691 kByte)
    We present and analyze a model for polycrystalline electrode surfaces based on an improved continuum model that takes finite ion size and solvation into account. The numerical simulation of finite size facet patterns allows to study two limiting cases: While for facet size diameter $d^facet to 0$ we get the typical capacitance of a spatially homogeneous but possible amorphous or liquid surface, in the limit $L^Debye << d^facet$ , an ensemble of non-interacting single crystal surfaces is approached. Already for moderate size of the facet diameters, the capacitance is remarkably well approximated by the classical approach of adding the single crystal capacities of the contributing facets weighted by their respective surface fraction. As a consequence, the potential of zero charge is not necessarily attained at a local minimum of capacitance, but might be located at a local capacitance maximum instead. Moreover, the results show that surface roughness can be accurately taken into account by multiplication of the ideally flat polycrystalline surface capacitance with a single factor. In particular, we find that the influence of the actual geometry of the facet pattern in negligible and our theory opens the way to a stochastic description of complex real polycrystal surfaces.

  • D.H. Doan, A. Fischer, J. Fuhrmann, A. Glitzky, M. Liero, Drift-diffusion simulation of S-shaped current-voltage relations for organic semiconductor devices, Preprint no. 2630, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2630 .
    Abstract, PDF (2299 kByte)
    We present an electrothermal drift-diffusion model for organic semiconductor devices with Gauss-Fermi statistics and positive temperature feedback for the charge carrier mobilities. We apply temperature dependent Ohmic contact boundary conditions for the electrostatic potential and discretize the system by a finite volume based generalized Scharfetter-Gummel scheme. Using path-following techniques we demonstrate that the model exhibits S-shaped current-voltage curves with regions of negative differential resistance, which were only recently observed experimentally.

  • M. Lübbering, J. Kunkel, P. Farrell, What company does my news article refer to? Tackling multiclass problems with topic modeling, Preprint no. 2621, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2621 .
    Abstract, PDF (354 kByte)
    While it is technically trivial to search for the company name to predict the company a new article refers to, it often leads to incorrect results. In this article, we compare the two approaches bag-of-words with k-nearest neighbors and Latent Dirichlet Allocation with k-nearest neighbor by assessing their applicability for predicting the S&P 500 company which is mentioned in a business news article or press release. Both approaches are evaluated on a corpus of 13k documents containing 84% news articles and 16% press releases. While the bag-of-words approach yields accurate predictions, it is highly inefficient due to its gigantic feature space. The Latent Dirichlet Allocation approach, on the other hand, manages to achieve roughly the same prediction accuracy (0.58 instead of 0.62) but reduces the feature space by a factor of seven.

  • C. Cancès, C. Chainais-Hillairet, J. Fuhrmann, B. Gaudeul, A numerical analysis focused comparison of several finite volume schemes for an unipolar degenerated drift-diffusion model, Preprint no. 2620, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2620 .
    Abstract, PDF (2725 kByte)
    In this paper, we consider an unipolar degenerated drift-diffusion system where the relation between the concentration of the charged species c and the chemical potential h is h(c) = log c/1-c. We design four different finite volume schemes based on four different formulations of the fluxes. We provide a stability analysis and existence results for the four schemes. The convergence proof with respect to the discretization parameters is established for two of them. Numerical experiments illustrate the behaviour of the different schemes.

  • H. Si, On decomposition of embedded prismatoids in ℝ³ without additional points, Preprint no. 2602, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2602 .
    Abstract, PDF (10 MByte)
    This paper considers three-dimensional prismatoids which can be embedded in ℝ³ A subclass of this family are twisted prisms, which includes the family of non-triangulable Scönhardt polyhedra [12, 10]. We call a prismatoid decomposable if it can be cut into two smaller prismatoids (which have smaller volumes) without using additional points. Otherwise it is indecomposable. The indecomposable property implies the non-triangulable property of a prismatoid but not vice versa.
    In this paper we prove two basic facts about the decomposability of embedded prismatoid in ℝ³ with convex bases. Let P be such a prismatoid, call an edge interior edge of P if its both endpoints are vertices of P and its interior lies inside P. Our first result is a condition to characterise indecomposable twisted prisms. It states that a twisted prism is indecomposable without additional points if and only if it allows no interior edge. Our second result shows that any embedded prismatoid in ℝ³ with convex base polygons can be decomposed into the union of two sets (one of them may be empty): a set of tetrahedra and a set of indecomposable twisted prisms, such that all elements in these two sets have disjoint interiors.

  • C.K. Macnamara, A. Caiazzo, I. Ramis-Conde, M.A.J. Chaplain, Computational modelling and simulation of cancer growth and migration within a 3D heterogeneous tissue: The effects of fibre and vascular structure, Preprint no. 2597, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2597 .
    Abstract, PDF (1351 kByte)
    The term cancer covers a multitude of bodily diseases, broadly categorised by having cells which do not behave normally. Since cancer cells can arise from any type of cell in the body, cancers can grow in or around any tissue or organ making the disease highly complex. Our research is focused on understanding the specific mechanisms that occur in the tumour microenvironment via mathematical and computational modeling. We present a 3D individual-based model which allows one to simulate the behaviour of, and spatio-temporal interactions between, cells, extracellular matrix fibres and blood vessels. Each agent (a single cell, for example) is fully realised within the model and interactions are primarily governed by mechanical forces between elements. However, as well as the mechanical interactions we also consider chemical interactions, for example, by coupling the code to a finite element solver to model the diffusion of oxygen from blood vessels to cells. The current state of the art of the model allows us to simulate tumour growth around an arbitrary blood-vessel network or along the striations of fibrous tissue.

  • V. John, P. Knobloch, U. Wilbrandt, Finite element pressure stabilizations for incompressible flow problems, Preprint no. 2587, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2587 .
    Abstract, PDF (2101 kByte)
    Discretizations of incompressible flow problems with pairs of finite element spaces that do not satisfy a discrete inf-sup condition require a so-called pressure stabilization. This paper gives an overview and systematic assessment of stabilized methods, including the respective error analysis.

  • A. Caiazzo, R. Maier, D. Peterseim, Reconstruction of quasi-local numerical effective models from low-resolution measurements, Preprint no. 2577, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2577 .
    Abstract, PDF (1550 kByte)
    We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on low-resolution measurements. We rely on recent quasi-local numerical effective models that, in contrast to conventional homogenized models, are provably reliable beyond periodicity assumptions and scale separation. The goal of this work is to show that the identification of the matrix representation of these effective models is possible. Algorithmic aspects of the inversion procedure and its performance are illustrated in a series of numerical experiments.

  • R. Schlundt, A multilevel Schur complement preconditioner with ILU factorization for complex symmetric matrices, Preprint no. 2556, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2556 .
    Abstract, PDF (318 kByte)
    This paper describes a multilevel preconditioning technique for solving complex symmetric sparse linear systems. The coefficient matrix is first decoupled by domain decomposition and then an approximate inverse of the original matrix is computed level by level. This approximate inverse is based on low rank approximations of the local Schur complements. For this, a symmetric singular value decomposition of a complex symmetric matix is used. The block-diagonal matrices are decomposed by an incomplete LDLT factorization with the Bunch-Kaufman pivoting method. Using the example of Maxwell's equations the generality of the approach is demonstrated.

  • L. Heltai, A. Caiazzo, Multiscale modeling of vascularized tissues via non-matching immersed methods, Preprint no. 2555, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2555 .
    Abstract, PDF (4085 kByte)
    We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two manifold) at a given pressure. We derive different variational formulations of the coupled problem, in which the effect of the vasculature can be surrogated in the elasticity equations via singular or hyper-singular forcing terms. These terms only depends on information defined on co-dimension two manifolds (such as vessel center line, cross sectional area, and mean pressure over cross section), thus drastically reducing the complexity of the computational model. We perform several numerical tests, ranging from simple cases with known exact solutions to the modeling of materials with random distributions of vessels. In the latter case, we use our immersed method to perform an in silico characterization of the mechanical properties of the effective biphasic material tissue via statistical simulations.

  • H. Si, On monotone sequences of directed flips, triangulations of polyhedra, and structural properties of a directed flip graph, Preprint no. 2554, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2554 .
    Abstract, PDF (2478 kByte)
    This paper studied the geometric and combinatorial aspects of the classical Lawson's flip algorithm  [21, 22]. Let A be a finite point set in R^2 and ω : A → R be a height function which lifts the vertices of A into R^3. Every flip in triangulations of A can be assigned a direction [6, Definition 6.1.1]. A sequence of directed flips is monotone if all its flips follow the same direction. We first established a relatively obvious relation between monotone sequences of directed flips on triangulations of A and triangulations of the lifted point set A^ω in R^3. We then studied the structural properties of a directed flip graph (a poset) on the set of all triangulations of A. We proved several general properties of this poset which clearly explain when Lawson's algorithm works and why it may fail in general. We further characterised the triangulations which cause failure of Lawson's algorithm, and showed that they must contain redundant interior vertices which are not removable by directed flips. A special case of this result in 3d has been shown in [19]. As an application, we described a simple algorithm to triangulate a special class of 3d non-convex polyhedra without using additional vertices. We prove sufficient conditions for the termination of this algorithm, and show it runs in O(n^3) time, where $n$ is the number of input vertices.

  • A. Jha, V. John, On basic iteration schemes for nonlinear AFC discretizations, Preprint no. 2533, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2533 .
    Abstract, PDF (814 kByte)
    Algebraic flux correction (AFC) finite element discretizations of steady-state convection-diffusion-reaction equations lead to a nonlinear problem. This paper presents first steps of a systematic study of solvers for these problems. Two basic fixed point iterations and a formal Newton method are considered. It turns out that the fixed point iterations behave often quite differently. Using a sparse direct solver for the linear problems, one of them exploits the fact that only one matrix factorization is needed to become very efficient in the case of convergence. For the behavior of the formal Newton method, a clear picture is not yet obtained.

  • J. Fuhrmann, C. Guhlke, B. Matejczyk, R. Müller, Transport of solvated ions in nanopores: Asymptotic models and numerical study, Preprint no. 2526, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2526 .
    Abstract, PDF (1233 kByte)
    Improved Poisson--Nernst--Planck systems taking into account finite ion size and solvation effects provide a more accurate model of electric double layers compared to the classical setting. We introduce and discuss several variants of such improved models. %Based on spatially fully resolved numerical models We study the effect of improved modeling in large aspect ratio nanopores. Moreover, we derive approximate asymptotic models for the improved Poisson--Nernst--Planck systems which can be reduced to one-dimensional systems. In a numerical study, we compare simulation results obtained from solution of the asymptotic 1D-models with those obtained by discretization of the full resolution models.

  • J. Fuhrmann, C. Guhlke, A. Linke, Ch. Merdon, R. Müller, Models and numerical methods for electrolyte flows, Preprint no. 2525, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2525 .
    Abstract, PDF (1807 kByte)
    The most common mathematical models for electrolyte flows are based on the dilute solution assumption, leading to a coupled system of the Nernst--Planck--Poisson drift-diffusion equations for ion transport and the Stokes resp. Navier--Stokes equations for fluid flow. This contribution discusses historical and recent model developments beyond the dilute solution assumption and focuses on the effects of finite ion sizes and solvation. A novel numerical solution approach is presented and verified here which aims at preserving on the discrete level consistency with basic thermodynamic principles and structural properties like independence of flow velocities from gradient contributions to external forces.

  • L.O. Müller, A. Caiazzo, P.J. Blanco, Reduced-order unscented Kalman filter in the frequency domain: Application to computational hemodynamics, Preprint no. 2484, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2484 .
    Abstract, PDF (1912 kByte)
    Objective: The aim of this work is to assess the potential of the reduced order unscented Kalman filter (ROUKF) in the context of computational hemodynamics, in order to estimate cardiovascular model parameters when employing real patient-specific data. Methods: The approach combines an efficient blood flow solver for one-dimensional networks (for the forward problem) with the parameter estimation problem cast in the frequency space. Namely, the ROUKF is used to correct model parameter after each cardiac cycle, depending on the discrepancies of model outputs with respect to available observations properly mapped into the frequency space. Results: First we validate the filter in frequency domain applying it in the context of a set of experimental measurements for an in vitro model. Second, we perform different numerical experiments aiming at parameter estimation using patient-specific data. Conclusion: Our results demonstrate that the filter in frequency domain allows a faster and more robust parameter estimation, when compared to its time domain counterpart. Moreover, the proposed approach allows to estimate parameters that are not directly related to the network but are crucial for targeting inter-individual parameter variability (e.g., parameters that characterize the cardiac output). Significance: The ROUKF in frequency domain provides a robust and flexible tool for estimating parameters related to cardiovascular mathematical models using in vivo data.

Vorträge, Poster

  • A. Maltsi, Th. Koprucki, T. Streckenbach, K. Tabelow, J. Polzehl, Model-based geometry reconstruction of quantum dots from TEM, Microscopy Conference 2019, Poster session IM 4, Berlin, September 1 - 5, 2019.

  • A. Maltsi, Th. Koprucki, T. Streckenbach, K. Tabelow, J. Polzehl, Model-based geometry reconstruction of quantum dots from TEM, BMS Summer School 2019: Mathematics of Deep Learning, Berlin, August 19 - 30, 2019.

  • N. Alia, On the simulation and optimization of the Navier--Stokes equations applied to buoyancy-driven liquid steel stirring, Workshop on Mathematics and Materials Science for Steel Production and Manufacturing, June 4 - 5, 2019, Thon Hotel Høyers, Skien, Norway, June 4, 2019.

  • P. Vágner, M. Pavelka, Dielectric polarization in GENERIC, Joint European Thermodynamics Conference (JETC 2019), Spain, May 21 - 24, 2019.

  • P. Vágner, Dielectric polarization in GENERIC, Conference to celebrate 80th jubilee of Miroslav Grmela, May 18 - 19, 2019, Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Prague, Czech Republic, May 18, 2019.

  • P. Vágner, Thermodynamic modeling of the YSZ metal gas electrode interface dynamics, University of Chemistry and Technology, Institute of Anorgani-Technology, Prague, Czech Republic, July 15, 2019.

  • P.P. Bawol , Ch. Merdon, H. Baltruschat, J. Fuhrmann, Rotating ring-disc electrode simulations: A comparison of classical finite differences to fully implicit finite volume scheme, ModVal 2019 - 16th Symposium on Modeling and Experimental Validation of Electrochemical Energy Technologies, March 12 - 13, 2019.

  • A. Caiazzo, Data assimilation in one-dimensional hemodynamics, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 36: Data-Driven Computational Fluid Dynamics (Part 2), September 30 - October 4, 2019, Eindhoven University of Technology, Netherlands, October 1, 2019.

  • A. Caiazzo, Geothermal reservoir: Modeling, simulation and optimization for district heating in hot sedimentary acquires, Leibniz MMS Days 2019, March 20 - 22, 2019, Universität Rostock , Leibniz-Institut für Atmosphärenphysik, Kühlungsborn, March 22, 2019.

  • A. Caiazzo, Multiscale hybrid modeling and simulation of cancer growth within a 3D heterogeneous tissue, Canada-Germany Workshop Mathematical Biology and Numerics, June 24 - 26, 2019, Universität Heidelberg, June 26, 2019.

  • P. Farrell, Creating anisotropic meshes by combining RBFs and HDE, International Conference of Kernel-based Methods and it's Application, October 10 - 14, 2019, Xi'an Jiaotong-Liverpool University, Suzhou, China, October 13, 2019.

  • P. Farrell, Highly accurate quadrature-based Scharfetter-Gummel schemes for charge transport in degenerates, International Congress on Industrial and Applied Mathematics (ICIAM), July 15 - 19, 2019, Valencia, Spain, July 19, 2019.

  • P. Farrell, Konjugierte Gradienten, Technische Universität Bergakademie Freiberg, Fakultät Mathematik und Informatik, November 27, 2019.

  • P. Farrell, Modeling and simulation of charge carrier transport in semiconductors and electrolytes, Pat II, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Institut für Silizium-Photovoltaik, June 27, 2019.

  • P. Farrell, Novel schemes for drift-diffusion semiconductor problems, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 15: Novel flux approximation schemes for advection-diffusion problems (Part 2), September 30 - October 4, 2019, Eindhoven University of Technology, Netherlands, October 2, 2019.

  • P. Farrell, Simulating semiconductor devices in a physically correct and stable way, Technische Universität Bergakademie Freiberg, Fakultät Mathematik und Informatik, November 27, 2019.

  • P. Farrell, Solving PDEs numerically, University of Exeter, Department of Mathematics, UK, April 11, 2019.

  • J. Fuhrmann, A. Linke, Ch. Merdon, R. Müller, Induced charge electroosmotic flow including finite ion size effects, 13th International Symposium on Electrokinetics (ELKIN), Cambridge, USA, June 12 - 14, 2019.

  • J. Fuhrmann, Entwicklung von Policies und Richtlinien für Forschungssoftware, deRSE19 - Konferenz für ForschungssoftwareentwicklerInnen in Deutschland, June 4 - 6, 2019, Albert Einstein Wissenschaftspark Potsdam.

  • J. Fuhrmann, Finite volume methods for degenerate drift-diffusion systems, Max-Planck-Institut für Eisenforschung GmbH, Defektchemie und Spektroskopie, Düsseldorf, October 14, 2019.

  • J. Fuhrmann, Induced charge electroosmotic flow including finite ion size effects, 13th International Symposium on Electrokinetics (ELKIN), June 12 - 14, 2019, Massachusetts Institute of Technology, Cambridge, USA, June 12, 2019.

  • J. Fuhrmann, Modeling and simulation of charge carrier transport in semiconductors and electrolytes, Pat I, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Institut für Silizium-Photovoltaik, June 27, 2019.

  • J. Fuhrmann, Modified exponential fitting schemes for degenerate semiconductors and electrolytes, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 15: Novel flux approximation schemes for advection-diffusion problems (Part 2), September 30 - October 4, 2019, Eindhoven University of Technology, Netherlands, October 2, 2019.

  • J. Fuhrmann, The Julia programming language in applications for electrochemical systems simulation, Leibniz MMS Days 2019, March 20 - 22, 2019, Universität Rostock , Leibniz-Institut für Atmosphärenphysik, Kühlungsborn, March 21, 2019.

  • J. Fuhrmann, n.n., Leibniz MMS Summer School 2019, October 28 - November 1, 2019, Mathematisches Forschungsinstitut Oberwolfach.

  • V. John, Algebraic finite element stabilizations for convection-diffusion equations, Workshop on Computational Modeling and Numerical Analysis (WCMNA 2019), February 25 - 28, 2019, Laboratório Nacional de Computação Científica, Petrópolis, Brazil, February 26, 2019.

  • V. John, Algebraic finite element stabilizations for convection-diffusion equations, Workshop ''Towards Computable Flows'', April 26 - 27, 2019, Georg-August-Universität Göttingen, Institut für Numerische und Angewandte Mathematik, April 26, 2019.

  • V. John, Finite element methods for incompressible flows, Workshop on Computational Modeling and Numerical Analysis (WCMNA 2019), February 25 - 28, 2019, Laboratório Nacional de Computação Científica, Petrópolis, Brazil.

  • V. John, Finite elements for scalar convection-dominated equations and incompressible flow problems -- A never ending story?, Conference on Applied Mathematics, August 19 - 21, 2019, Lahore University of Management Sciences, Pakistan, August 19, 2019.

  • V. John, On $L^2(Omega)$ estimates for finite element methods for evolutionary convection-dominated problems, PIMS-Germany Workshop on Discretization of Variational Eigenvalue and Flow Problems, June 24 - 26, 2019, Universität Heidelberg, June 25, 2019.

  • V. John, Variational Multiscale (VMS) methods for the simulation of turbulent incompressible flows, University of Groningen, Bernoulli Institute, Computational Mechanics & Numerical Mathematics, Netherlands, September 23, 2019.

  • V. John, n.n., Indo-German Conference on Computational Mathematics (IGCM), December 2 - 4, 2019, Indian Institute of Science, Department of Computer and Data Sciences, Bangalore, India.

  • A. Linke, On high Reynolds number flows, pressure-robustness and high-order methods, International Congress on Industrial and Applied Mathematics (ICIAM), July 15 - 19, 2019, Valencia, Spain, July 17, 2019.

  • A. Linke, On high Reynolds number flows, pressure-robustness and high-order methods, Technische Universität Darmstadt, Fachbereich Mathematik, August 28, 2019.

  • A. Linke, On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond, Conference "POEMs --- POlytopal Element Methods in Mathematics and Engineering'', April 29 - May 3, 2019, CIRM - Luminy, Centre International de Rencontres Mathématiques, Marseille, France, April 29, 2019.

  • A. Linke, On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 23: Recent Advances in Numerical Simulation of Incompressible Flows (Part 3), September 30 - October 4, 2019, Eindhoven University of Technology, Netherlands, October 2, 2019.

  • A. Linke, On pressure-robustness, coherent structures and vortex-dominated flows, Leibniz MMS Days 2019, March 20 - 22, 2019, Universität Rostock , Leibniz-Institut für Atmosphärenphysik, Kühlungsborn, March 22, 2019.

  • A. Linke, Pressure-robustness -- A new criterion for the accuracy of incompressible Navier--Stokes solvers at high Reynolds number and beyond, 4th Annual SU2 Developers Meeting, May 8 - 10, 2019, Villa Monastero, Varenna, Italy, May 9, 2019.

  • A. Linke, Robust discretization of advective linear transport, based on a complexte flux scheme and entropy principles, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 15: Novel flux approximation schemes for advection-diffusion problems (Part 1), September 30 - October 4, 2019, Eindhoven University of Technology, Netherlands, October 2, 2019.

  • A. Linke, n.n., Leibniz MMS Summer School 2019, October 28 - November 1, 2019, Mathematisches Forschungsinstitut Oberwolfach.

  • A. Linke, tba., PIMS-Germany Workshop on Discretization of Variational Eigenvalue and Flow Problems, June 24 - 26, 2019, Universität Heidelberg.

  • A. Linke , Towards a pressure robust computation of computable flows, Workshop ''Towards Computable Flows'', April 26 - 27, 2019, Georg-August-Universität Göttingen, Institut für Numerische und Angewandte Mathematik, April 27, 2019.

  • CH. Merdon, A gradient-robust, well-balanced discretisation for the compressible barotropic Stokes problem, European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2019), Minisymposium 23: Recent Advances in Numerical Simulation of Incompressible Flows (Part 1), September 30 - October 4, 2019, Eindhoven University of Technology, Netherlands, October 1, 2019.

  • CH. Merdon, Pressure-robust finite element discretisations for the Navier--Stokes problem, Technische Universität Dresden, Fachbereich Mathematik, April 11, 2019.

  • CH. Merdon, Pressure-robust mixed finite element methods and refined a posteriori error control for the Stokes problem, Georg-August-Universität Göttingen, Institut für Numerische und Angewandte Mathematik, January 29, 2019.

  • CH. Merdon, Pressure-robustness in the discretisation of the Navier--Stokes equations --- An overview, International Congress on Industrial and Applied Mathematics (ICIAM), July 15 - 19, 2019, Valencia, Spain, July 17, 2019.

  • H. Si, An introduction to mesh generation methods and softwares for scientific computing, December 15 - 26, 2019, Zhejiang University, Center for Engineering & Scientific Computation, Hangzhou, China.

  • H. Si, Instructor for the cours ``An Introduction to Mesh Generation Methods and Software for Scientific Computing'', BAIHANG International Summer School 2019, July 1 - 26, 2019, Beihang University, China.

  • P. Vágner, A detailed double layer model of solid oxide cell electrolyte-electrode interface, ModVal 2019 - 16th Symposium on Modeling and Experimental Validation of Electrochemical Energy Technologies, March 12 - 13, 2019.

  • A. Maltsi, Th. Koprucki, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Computing TEM images of semiconductor nanostructures, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), WIAS Berlin, October 8 - 10, 2018.

  • N. Alia, Modeling and optimization of a gas-stirred liquid flow for steelmaking processes, The 20th European Conference on Mathematics for Industry (ECMI), MS27: MSO for steel production and manufacturing, June 18 - 22, 2018, University Budapest, Institute of Mathematics at Eötvös Loránd, Hungary, June 19, 2018.

  • D.H. Doan, J. Fuhrmann, A. Glitzky, Th. Koprucki, M. Liero, On van Roosbroeck systems with Gauss--Fermi statistics, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), WIAS Berlin, October 8 - 10, 2018.

  • R. Müller, J. Fuhrmann, C. Guhlke, B. Matejczyk , Dimension reduction of improved Nernst--Planck models for charged nanopores, Asymptotic Behavior of Systems of PDE Arising in Physics and Biology: Theoretical and Numerical Points of View (ABPDE III), Lille, France, August 28 - 31, 2018.

  • R. Ahrens, F. Anker, C. Bartsch, A. Voigt, V. Wiedmeyer, K. Sundmacher, V. John, S. Le Borne, Advanced numerical methods for the simulation of population balance systems, 6th International Conference on Population Balance Modelling (PBM2018), Ghent University, Belgium, May 7 - 9, 2018.

  • C. Cancès, C. Chainais-Hillairet, J. Fuhrmann, B. Gaudeul, Numerical schemes for a reduced case of an improved Nernst--Planck--Poisson model, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), WIAS Berlin, October 8 - 10, 2018.

  • P. Farrell, D. Peschka, Challenges for drift-diffusion simulations of semiconductors: A comparative study of different discretization philosophies, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), WIAS Berlin, October 8 - 10, 2018.

  • H. Si, Herbert's contributions in delaunay mesh generation and some related problems, Workshop ``HerbertFest to celebrate Prof. Herbert Edelsbrunner's 60th Birthday'', June 20 - 21, 2018, Institute of Science and Technology Austria, Klosterneuburg, Austria, June 20, 2018.

  • L. Blank, A robust finite element method for the Brinkman problem, 13th International Workshop on Variational Multiscale and Stabilized Finite Elemements, Weierstraß-Institut, Berlin, December 5, 2018.

  • L. Blank, An unconditionally stable, low order, and robust finite element method for the numerical simulation of porous media flow, 39th Northern German Colloquium on Applied Analysis and Numerical Mathematics (NoKo 2018), June 1 - 2, 2018, Technische Universität Braunschweig, June 2, 2018.

  • Z. Lakdawala, Mathematics meets industry -- Modeling and simulation of plain and porous media, Habib University, Dhanani School of Science and Engineering, Karachi, Pakistan, November 27, 2018.

  • Z. Lakdawala, Multiscale modeling of filtration processes, Quaid-i-Azam University, Department of Mathematics, Islamabad, Pakistan, November 29, 2018.

  • C. Bartsch, V. John, R.I.A. Patterson, A new mixed stochastic-deterministic simulation approach to particle populations in fluid flows, 6th International Conference on Population Balance Modelling (PBM2018), Ghent University, Belgium, May 7 - 9, 2018.

  • A. Caiazzo, A benchmark study for CFD solvers: Simulation of air flow in livestock husbandry, 3rd Leibniz MMS Days 2018, February 28 - March 2, 2018, Wissenschaftszentrum Leipzig, February 28, 2018.

  • A. Caiazzo, A penalty-free Nitsche method for the Stokes, Darcy and Brinkman problems, Universität Augsburg, Lehrstuhl für Numerische Mathematik, May 15, 2018.

  • A. Caiazzo, Mathematical modeling and simulations of geothermal reservoirs, Virtual Physiological Human Conference (VPH2018), September 5 - 7, 2018, University of Zaragoza, Spain, September 6, 2018.

  • A. Caiazzo, Mathematical modeling and simulations of geothermal reservoirs, 16th European Finite Element Fair (EFEF 2018), June 8 - 9, 2018, Universität Heidelberg,, June 8, 2018.

  • A. Caiazzo, Mathematical modeling and simulations of geothermal reservoirs, Leibniz-Institut für Angewandte Geophysik, Hannover, November 7, 2018.

  • A. Caiazzo, Multiscale and reduced-order modeling of biphasic materials with application to tissue elastography, Rheinische Friedrich-Wilhelms-Universität Bonn, Institut für Numerische Simulation, November 23, 2018.

  • A. Caiazzo, Multiscale modeling of individual-based cancer models with arbitrary vasculature and fiber structure, 6th European Conference on Computational Mechanics, 7th European Conference on Computational Fluid Dynamics (ECCM-ECFD 2018), June 11 - 15, 2018, University of Glasgow, UK, June 12, 2018.

  • A. Caiazzo, Robust open boundary conditions and efficient data assimilation in multiscale hemodynamics, International Symposium ``Modeling, Simulation and Optimization of the Cardiovascular System'', October 22 - 24, 2018, Universität Magdeburg, October 22, 2018.

  • A. Caiazzo, Towards the personalization of (1D) blood-flow simulations, University of Amsterdam, Computational Science Lab, Netherlands, September 21, 2018.

  • W. Dreyer, Non-Newtonian fluids and the 2nd law of thermodynamics, 3rd Leibniz MMS Days 2018, February 28 - March 2, 2018, Wissenschaftszentrum Leipzig, March 1, 2018.

  • W. Dreyer, Thermodynamics and kinetic theory of non-Newtonian fluids, Technische Universität Darmstadt, Mathematische Modellierung und Analysis, June 13, 2018.

  • J. Fuhrmann, A. Linke, Ch. Merdon, C. Guhlke, R. Müller, Models and numerical methods for electroosmotic flow including finite ion size effects, Workshop on Ion Exchange Membranes for Energy Applications (EMEA2018), Bad Zwischenahn, June 26 - 28, 2018.

  • J. Fuhrmann, A. Linke, Ch. Merdon, C. Guhlke, R. Müller, Models and numerical methods for electroosmotic flow including finite ion size effects, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), WIAS Berlin, October 8 - 10, 2018.

  • J. Fuhrmann, Computational assessment of the derivation of the Butler--Volmer kinetics as a limit case of the Nernst--Planck equations with surface reactions, Workshop ``Numerical Optimization of the PEM Fuel Cell Bipolar Plate'', Zentrum für Solarenergie- und Wasserstoff-Forschung (ZSW), Ulm, March 20, 2018.

  • J. Fuhrmann, Coupled finite volumes/finite elements for electroosmotic flow with solvation effects, Université de Lille, Centre Européen pour les Mathématiques, France, May 17, 2018.

  • J. Fuhrmann, Handling research software: Recommendations to users, developers and research managers, 3rd Leibniz MMS Days 2018, February 28 - March 2, 2018, Wissenschaftszentrum Leipzig, March 1, 2018.

  • J. Fuhrmann, Models and numerical methods for electroosmotic flow with finite ion size effect, International Workshop ``Physics of Membrane Processes'' (PMP2018), September 2, 2018, Nuovo Polo Congressuale Bologna, Italy, September 2, 2018.

  • J. Fuhrmann, Numerical methods for electroosmotic flow including finite ion size effects, 69th Annual Meeting of the International Society of Electrochemistry, September 2 - 7, 2018, International Society of Electrochemistry, Nuovo Polo Congressuale Bologna, Italy, September 6, 2018.

  • J. Fuhrmann, Robust quality preserving numerical methods for electroosmotic flows, 15th Symposium on Modeling and Validation of Electrochemical Energy Devices, April 12 - 13, 2018, Paul Scherrer Institut, Aarau, Switzerland, April 12, 2018.

  • J. Fuhrmann, Thermodynamically consistent models and numerical methods for electroosmotic flow, Tschechische Technische Universität Prag, Czech Republic, February 19, 2018.

  • J. Fuhrmann, Thermodynamically consistent finite volumes and pressure robust finite elements for electroosmotic flow, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), March 21 - 23, 2018, Technische Universität München, March 22, 2018.

  • J. Fuhrmann, Towards finite volume based PDE simulations with Julia, Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic, December 19, 2018.

  • J. Fuhrmann, Voronoi finite volumes and pressure robust finite elements for electrolyte models with finite ion sizes, 9th International Conference ``Numerical Geometry, Grid Generation and Scientific Computing'' (NUMGRID 2018), December 1 - 5, 2018, Russian Academy of Sciences, Federal Research Center of Information and Control, Moscow, Russian Federation, December 3, 2018.

  • V. John, A new mixed stochastic-deterministic simulation approach for particle populations in fluid flows, 6th European Seminar on Computing (ESCO), June 3 - 8, 2018, University of West Bohemia, Pilsen, Czech Republic, June 6, 2018.

  • V. John, Angewandte Mathematik für Strömungssimulationen, Martin-Luther-Universität Halle, Fachbereich Mathematik, October 27, 2018.

  • V. John, Finite elements for scalar convection-dominated equations and incompressible flow problems -- A never ending story?, International Conference of Boundary and Interior Layers (BAIL 2018), June 18 - 22, 2018, University of Strathclyde, Glasgow, Scotland, UK, June 18, 2018.

  • V. John, Variational Multiscale (VMS) methods for the simulation of turbulent incompressible flows, University of Strathclyde, Department of Mathematics and Statistics, Glasgow, UK, November 14, 2018.

  • A. Linke, On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond, 13th International Workshop on Variational Multiscale and Stabilized Finite Elemements, Weierstraß-Institut, Berlin, December 5, 2018.

  • A. Linke, On the role of the Helmholtz--Hodge projector for a novel pressure-robust discretization theory for the incompressible Navier--Stokes equations, The University of Texas at Austin, Institute for Computational Engineering and Scienses, USA, September 18, 2018.

  • A. Linke, On the role of the Helmholtz--Leray projector for a novel pressure-robust discretization theory for the incompressible Navier--Stokes equations, Workshop ``Finite Element Exterior Calculus (FEEC) and High Order Methods'', June 4 - 6, 2018, University of Oslo, Faculty of Mathematics and Natural Sciences, Norway, June 6, 2018.

  • A. Linke, On the role of the Helmholtz--Leray projector for a novel pressure-robust discretization theory for the incompressible Navier--Stokes equations, Georg-August-Universität Göttingen, Institut für Numerische und Angewandte Mathematik, January 23, 2018.

  • A. Linke, On the role of the Helmholtz--Leray projector for a novel pressure-robust discretization theory for the incompressible Navier--Stokes equations, Aix Marseille Université, Institut de Mathématiques, France, April 3, 2018.

  • A. Linke, On the role of the Helmholtz--Leray projector for a novel pressure-robust discretization theory for the incompressible Navier--Stokes equations, Clemson University, Department of Mathematical Sciences, South Carolina, USA, August 17, 2018.

  • A. Linke, On the role of the Helmholtz--Leray projector in the space discretization of the Navier--Stokes equations, 3rd Leibniz MMS Days 2018, February 28 - March 2, 2018, Wissenschaftszentrum Leipzig, March 1, 2018.

  • A. Linke, Towards pressure-robust mixed methods for the incompressible Navier--Stokes equations, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), March 19 - 23, 2018, Technische Universität München, March 22, 2018.

  • A. Linke, User talk: Pressure-robust space discretization for the incompressible Navier--Stokes equations, 2nd NGSolve User Meeting, July 4 - 6, 2018, Georg-August-Universität Göttingen, Institut für Numerische und Angewandte Mathematik, July 5, 2018.

  • CH. Merdon, Well-balanced discretisation of the compressible Stokes problem, 13th International Workshop on Variational Multiscale and Stabilized Finite Elemements, Weierstraß-Institut, Berlin, December 6, 2018.

  • H. Si, A construction of anisotropic meshes based on quasi conformal mapping, 27th International Meshing Roundtable and User Forum ``Mesh Modeling for Simulations and Visualization'', October 1 - 5, 2018, Albuquerque, New Mexiko, USA, October 3, 2018.

  • H. Si, Advances in unstructured mesh generation and adaptation, International Workshop on Numerical Analysis with Applications in Medium Imaging and Computer Visions, Minisymposium ``Computer Vision and Applications'', December 10 - 14, 2018, International Consortium of Chinese Mathematicians in Computational and Applied Mathematics (ICCM-CAM), Shing-Tung Yau Center of the Southeast University, Nanjing, China, December 13, 2018.

  • H. Si, An algorithm to triangulate 3D non-convex polyhedra without Steiner points, 9th International Conference ``Numerical Geometry, Grid Generation and Scientific Computing'' (NUMGRID 2018), December 3 - 9, 2018, Russian Academy of Sciences, Federal Research Center of Information and Control, Moscow, Russian Federation, December 3, 2018.

  • H. Si, Challenges in 3D unstructured mesh generation and adaptation, Challenges in the Computational Modeling of Beijing's Air Pollution and Traffic, March 19 - 23, 2018, Beijing University of Technology, China, March 22, 2018.

  • H. Si, Challenges in 3D unstructured mesh generation and adaptation, The Second Chinese International Conference on CFD, July 17 - 21, 2018, China Aerodynamics Research and Development Center, Mianyang, Sichuan, China, July 20, 2018.

  • H. Si, Unstructured mesh generation and its applications, University of Cambridge, Bullard Laboratories, UK, October 18, 2018.

  • P. Vágner, Formulation of non-equilibrium irreversible electro-magneto-thermodynamics within GENERIC with applications in electrochemistry, 8th International Workshop on Nonequilibrium Thermodynamics 2018 (IWNET 2018), July 2 - 6, 2018, Eindhoven University of Technology, De Ruwenberg Hotel and Conference Center, Sint-Michielsgestel, Netherlands, July 4, 2018.

  • U. Wilbrandt, An assessment of some solvers for saddle point problems emerging from the incompressible Navier--Stokes equations, 13th International Workshop on Variational Multiscale and Stabilized Finite Elemements, Weierstraß-Institut, Berlin, December 7, 2018.

  • U. Wilbrandt, Iterative subdomain methods for the Stokes--Darcy coupling, 6th European Conference on Computational Mechanics, 7th European Conference on Computational Fluid Dynamics (ECCM-ECFD 2018), June 11 - 15, 2018, University of Glasgow, UK, June 11, 2018.

Preprints im Fremdverlag

  • J. Fuhrmann, C. Guhlke, Ch. Mehrdon, A. Linke, R. Müller, Induced charge electroosmotic flow with finite ion size and solvation effects, Preprint no. arXiv:1901.06941, Cornell University, 2019, DOI 10.1016/j.electacta.2019.05.051 .

  • A. Linke, Ch. Merdon, M. Neilan, Pressure-robustness in quasi-optimal a priori estimates for the Stokes problem, Preprint no. arxiv.org/abs/1906.03009, Cornell University Library, arXiv.org, 2019.

  • N. Alia, V. John, S. Ollila, Re-visiting the single-phase flow model for liquid steel ladle stirred by gas, Preprint no. arXiv.1811.11535, Cornell University Library, arXiv.org, 2018, DOI 10.1016/j.apm.2018.11.005 .
    Abstract
    Ladle stirring is an important step of the steelmaking process to homogenize the temperature and the chemical composition of the liquid steel and to remove inclusions before casting. Gas is injected from the bottom of the bath to induce a turbulent flow of the liquid steel. Multiphase modeling of ladle stirring can become computationally expensive, especially when used within optimal flow control problems. This paper focuses therefore on single-phase flow models. It aims at improving the existing models from the literature. Simulations in a 2d axial-symmetrical configuration, as well as, in a real 3d laboratory-scale ladle, are performed. The results obtained with the present model are in a relative good agreement with experimental data and suggest that it can be used as an efficient model in optimal flow control problems.

  • N.R. Gauger, A. Linke, P. Schroeder, On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond, Preprint no. arXiv:1808.10711, Cornell University Library, arXiv.org, 2018.
    Abstract
    Recently, high-order space discretisations were proposed for the numerical simulation of the incompressible Navier--Stokes equations at high Reynolds numbers, even for complicated domains from simulation practice. Although the overall spatial approximation order of the algorithms depends on the approximation quality of the boundary (often not better than third order), competitively accurate and efficient results were reported. In this contribution, first, a possible explanation for this somewhat surprising result is proposed: the velocity error of high-order space discretisations is more robust against quantitatively large and complicated pressure fields than low-order methods. Second, it is demonstrated that novel pressure-robust methods are significantly more accurate than comparable classical, non-pressure-robust space discretisations, whenever the quadratic, nonlinear convection term is a nontrivial gradient field like in certain generalised Beltrami flows at high Reynolds number. Then, pressure-robust methods even allow to halve the (formal) approximation order without compromising the accuracy. Third, classical high-order space discretisations are outperformed by pressure-robust methods whenever the boundary is not approximated with high-order accuracy. This improved accuracy of (low-order) pressure-robust mixed methods is explained in terms of a Helmholtz--Hodge projector, which cancels out the nonlinear convection term in any generalised Beltrami flow, since it is a gradient field. The numerical results are illustrated by a novel numerical analysis for pressure-robust and classical space discretisations. Further, the relevance of these results is discussed for flows that are not of Beltrami type.