Publications
Monographs

U. Wilbrandt, StokesDarcy 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. iviii, 1211, (Monograph Published), DOI 10.1007/9783030029043 .

A. Caiazzo, I.E. VignonClementel, Mathematical modeling of blood flow in the cardiovascular system, I. Sack, T. Schaeffter, eds., Quantification of Biophysical Parameters in Medical Imaging, Springer, Cham, 2018, pp. 4570, (Chapter Published), DOI 10.1007/9783319659244_3 .
Articles in Refereed Journals

P.W. Schroeder, V. John, P.L. Lederer, Ch. Lehrenfeld, G. Lube, J. Schöberl, On reference solutions and the sensitivity of the 2D KelvinHelmholtz instability problem, Computers & Mathematics with Applications. An International Journal, 77 (2019), pp. 10101028.

C. Bartsch, V. John, R.I.A. Patterson, Simulations of an ASA flow crystallizer with a coupled stochasticdeterministic approach, Comput. Chem. Engng., 124 (2019), pp. 350363, 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 socalled kinetic MonteCarlo 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. 
M. Radziunas, J. Fuhrmann, A. Zeghuzi, H.J. Wünsche, Th. Koprucki, C. Brée, H. Wenzel, U. Bandelow, Efficient coupling of electrooptical and heattransport models for highpower broadarea semiconductor lasers, Optical and Quantum Electronics, 51 (2019), published online on 22.02.2019, DOI 10.1007/s1108201917921 .
Abstract
In this work, we discuss the modeling of edgeemitting highpower broadarea semiconductor lasers. We demonstrate an efficient iterative coupling of a slow heat transport (HT) model defined on multiple verticallateral laser crosssections with a fast dynamic electrooptical (EO) model determined on the longitudinallateral domain that is a projection of the device to the active region of the laser. Whereas the HTsolver calculates temperature and thermallyinduced refractive index changes, the EOsolver exploits these distributions and provides timeaveraged field intensities, quasiFermi potentials, and carrier densities. All these timeaveraged distributions are used repetitively by the HTsolver for the generation of the heat sources entering the HT problem solved in the next iteration step. 
N. Alia, V. John, S. Ollila, Revisiting the singlephase 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. 549556 (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 manyparticle model for LFP electrodes, Continuum Mechanics and Thermodynamics, 30 (2018), pp. 593628, DOI 10.1007/s0016101806297 .
Abstract
In the framework of nonequilibrium 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 lithiumpoor to a lithiumrich 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 voltagecurrent 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 graddiv stabilization in DG methods for incompressible flows: Limiting behavior and extension to tensorproduct meshes, Computer Methods in Applied Mechanics and Engineering, 341 (2018), pp. 917938, DOI 10.20347/WIAS.PREPRINT.2448 .
Abstract
Graddiv 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 graddiv 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 measurevalued 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 convectiondiffusion equations, SeMA Journal. Boletin de la Sociedad Espannola de Matematica Aplicada, 75 (2018), pp. 655685, DOI 10.1007/s4032401801606 .

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. 25332565, DOI 10.1007/s4031401704638 .

F. Dassi, L. Kamenski, P. Farrell, H. Si, Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction, ComputerAided Design, 103 (2018), pp. 213, DOI 10.1016/j.cad.2017.11.010 .
Abstract
Given a tetrahedral mesh and objective functionals measuring the mesh quality which take into account the shape, size, and orientation of the mesh elements, our aim is to improve the mesh quality as much as possible. In this paper, we combine the moving mesh smoothing, based on the integration of an ordinary differential equation coming from a given functional, with the lazy flip technique, a reversible edge removal algorithm to modify the mesh connectivity. Moreover, we utilize radial basis function (RBF) surface reconstruction to improve tetrahedral meshes with curved boundary surfaces. Numerical tests show that the combination of these techniques into a mesh improvement framework achieves results which are comparable and even better than the previously reported ones. 
A. Horn, A. Li, T.A. Dembek, A. Kappel, C. Boulay, H. Si, ET AL., LeadDBS v2: Towards a comprehensive pipeline for deep brain stimulation imaging, NeuroImage, 1 (2018), pp. 293316, DOI 10.1016/j.neuroimage.2018.08.068 .

M. Patriarca, P. Farrell, J. Fuhrmann, Th. Koprucki, Highly accurate quadraturebased ScharfetterGummel 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. 4049 (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 driftdiffusion problems in degenerate semiconductors with nonBoltzmann 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 quadraturebased ScharfetterGummel 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 stateoftheart 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 infsup stable FEM applied to the timedependent incompressible NavierStokes equations, SeMA Journal. Boletin de la Sociedad Espannola de Matematica Aplicada, 75 (2018), pp. 629653, DOI 10.1007/s4032401801571 .
Abstract
Infsup stable FEM applied to timedependent incompressible NavierStokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressurerobustness ensures the fulfilment of a fundamental invariance principle and velocity error estimates are not corrupted by the pressure approximability. Secondly, Resemirobustness means that constants appearing on the righthand 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 Resemirobust estimates for pointwise divergencefree H1conforming FEM (like ScottVogelius pairs or certain isogeometric based FEM) and pointwise divergencefree H(div)conforming discontinuous Galerkin FEM. For convectiondominated problems, the latter naturally includes an upwind stabilisation for the velocity which is not gradientbased. 
J. DE Frutos, B. Garc'iaArchilla, V. John, J. Novo, Analysis of the graddiv stabilization for the timedependent NavierStokes equations with infsup stable finite elements, Advances in Computational Mathematics, 44 (2018), pp. 195225.

N. Ahmed, C. Bartsch, V. John, U. Wilbrandt, An assessment of solvers for some saddle point problems emerging from the incompressible NavierStokes equations, Computer Methods in Applied Mechanics and Engineering, 331 (2018), pp. 492513, DOI 10.1016/j.cma.2017.12.004 .
Abstract
Efficient incompressible flow simulations, using infsup 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 steadystate and timedependent flows around cylinders in 2d and 3d. Several pairs of infsup stable finite element spaces with second order velocity and first order pressure are used. It turns out that for the steadystate problems often FGMRES with an appropriate multigrid preconditioner was the most efficient method on finer grids. For the timedependent 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 GalerkinPetrov method for incompressible flow problems, Applied Mathematics and Computation, 333 (2018), pp. 304324, DOI 10.1016/j.amc.2018.03.088 .
Abstract
The local projection stabilization (LPS) method in space is considered to approximate the evolutionary Oseen equations. Optimal error bounds independent of the viscosity parameter are obtained in the continuousintime case for the approximations of both velocity and pressure. In addition, the fully discrete case in combination with higher order continuous GalerkinPetrov (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 timeindependent. Numerical results show that the predicted order is also achieved in the general case of timedependent convective terms. 
N. Ahmed, A. Linke, Ch. Merdon, On really lockingfree mixed finite element methods for the transient incompressible Stokes equations, SIAM Journal on Numerical Analysis, 56 (2018), pp. 185209.
Abstract
Infsup stable mixed methods for the steady incompressible Stokes equations that relax the divergence constraint are often claimed to deliver lockingfree discretizations. However, this relaxation leads to a pressuredependent 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 lockingfree, 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. Semidiscrete and fullydiscrete apriori velocity and pressure error estimates are derived, which show beautiful robustness properties. Two numerical examples illustrate the superior accuracy of pressurerobust space discretizations in the case of small viscosities. 
W. Dreyer, C. Guhlke, R. Müller, Bulksurface electrothermodynamics and applications to electrochemistry, Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies, 20 (2018), pp. 939/1939/44, 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 FermiDirac and GaussFermi statistics, Optical and Quantum Electronics, (2018), published online on 07.02.2018, DOI 10.1007/s1108201813498 .
Abstract
We compare three thermodynamically consistent ScharfetterGummel schemes for different distribution functions for the carrier densities, including the FermiDirac integral of order 1/2 and the GaussFermi integral. The most accurate (but unfortunately also most costly) generalized ScharfetterGummel 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 FermiDirac and GaussFermi statistics. Finally, by comparing two modified (diffusionenhanced and inverse activity based) ScharfetterGummel schemes with the more accurate generalized scheme, we show that the diffusionenhanced ansatz leads to considerably lower flux errors, confirming previous results (J. Comp. Phys. 346:497513, 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. 677698, DOI 10.20347/WIAS.PREPRINT.2403 .
Abstract
A mantle convection model consisting of the stationary Stokes equations and a timedependent convectiondiffusion equation for the temperature is studied. The Stokes problem is discretized with a conforming infsup 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 convectiondominated equations and incompressible flow problems  A never ending story?, Computing and Visualization in Science, 19 (2018), pp. 4763.
Abstract
The contents of this paper is twofold. First, important recent results concerning finite element methods for convectiondominated 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, Quasioptimality of a pressurerobust nonconforming finite element method for the Stokes problem, Mathematics of Computation, 87 (2018), pp. 15431566, DOI 10.1090/mcom/3344 .
Abstract
Nearly all classical infsup stable mixed finite element methods for the incompressible Stokes equations are not pressurerobust, i.e., the velocity error is dependent on the pressure. However, recent results show that pressurerobustness can be recovered by a nonstandard 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 pressurerobust scheme with low regularity. The numerical analysis applies divergencefree H¹conforming Stokes finite element methods as a theoretical tool. As an example, pressurerobust velocity and pressure apriori error estimates will be presented for the (first order) nonconforming CrouzeixRaviart 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.
Contributions to Collected Editions

M. Patriarca, P. Farrell, J. Fuhrmann, Th. Koprucki, M. Auf DER Maur, Highly accurate discretizations for nonBoltzmann 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, 2018, pp. 5354.

TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Towards modelbased 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, 2018, pp. 115116.

M. Radziunas, J. Fuhrmann, A. Zeghuzi, H.J. Wünsche, Th. Koprucki, H. Wenzel, U. Bandelow, Efficient coupling of heat flow and electrooptical models for simulation of dynamics in highpower broadarea semiconductor devices, 18th International Conference on Numerical Simulation of Optoelectronic Devices, Hong Kong, China, November 5  9, 2018, J. Piprek, A.B. Djurisic, eds., IEEE, 2018, pp. 9192.
Preprints, Reports, Technical Reports

A. Caiazzo, R. Maier, D. Peterseim, Reconstruction of quasilocal numerical effective models from lowresolution 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 lowresolution measurements. We rely on recent quasilocal 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 blockdiagonal matrices are decomposed by an incomplete LDL^{T} factorization with the BunchKaufman 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 nonmatching 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 threedimensions) and a thin vascular structure (treated as a codimension 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 hypersingular forcing terms. These terms only depends on information defined on codimension 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 nonconvex 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. 
W. Dreyer, C. Guhlke, R. Müller, The impact of solvation and dissociation on the transport parameters of liquid electrolytes: Continuum modeling and numerical study, Preprint no. 2539, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2539 .
Abstract, PDF (1472 kByte)
Electrothermodynamics 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 ionsolvent 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 MaxwellStefan setting and incorporate them into the general electrothermodynamic 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 nondilute electrolyte. 
A. Linke, L.G. Rebholz, Pressureinduced locking in mixed methods for timedependent (Navier)Stokes equations, Preprint no. 2534, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2534 .
Abstract, PDF (227 kByte)
We consider infsup stable mixed methods for the timedependent incompressible Stokes and NavierStokes equations, extending earlier work on the steady (Navier)Stokes Problem. A locking phenomenon is identified for classical infsup stable methods like the TaylorHood or the CrouzeixRaviart 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 L^{2} convergence order for high order methods, and even a complete stall of the L^{2} convergence order for lowestorder methods on preasymptotic meshes is predicted by the analysis and practically observed. On the other hand, it is also shown that (structurepreserving) pressurerobust mixed methods do not suffer from this locking phenomenon, even if they are of lowestorder. A connection to wellbalanced schemes for (vectorial) hyperbolic conservation laws like the shallow water or the compressible Euler equations is made. 
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 steadystate convectiondiffusionreaction 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 PoissonNernstPlanck 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 PoissonNernstPlanck systems which can be reduced to onedimensional systems. In a numerical study, we compare simulation results obtained from solution of the asymptotic 1Dmodels 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 NernstPlanckPoisson driftdiffusion equations for ion transport and the Stokes resp. NavierStokes 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. 
H. Stephan, A. Stephan, Memory equations as reduced Markov processes, Preprint no. 2496, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2496 .
Abstract, PDF (315 kByte)
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 oneway 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. 
L. Blank, A. Caiazzo, F. Chouly, A. Lozinski, J. Mura, Analysis of a stabilized penaltyfree Nitsche method for the Brinkman, Stokes, and Darcy problems, Preprint no. 2489, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2489 .
PDF (857 kByte) 
P. Farrell, D. Peschka, Challenges for driftdiffusion simulations of semiconductors: A comparative study of different discretization philosophies, Preprint no. 2486, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2486 .
Abstract, PDF (2457 kByte)
We analyze and benchmark the error and the convergence order of finite difference, finiteelement as well as Voronoi finitevolume discretization schemes for the driftdiffusion 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 Lshaped 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. 
L.O. Müller, A. Caiazzo, P.J. Blanco, Reducedorder 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 patientspecific data. Methods: The approach combines an efficient blood flow solver for onedimensional 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 patientspecific 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 interindividual 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.
Talks, Poster

P.P. Bawol , Ch. Merdon, H. Baltruschat, J. Fuhrmann, Rotating ringdisc 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, Geothermal reservoir: Modeling, simulation and optimization for district heating in hot sedimentary acquires, Leibniz MMS Days 2019, March 20  22, 2019, Universität Rostock , LeibnizInstitut für Atmosphärenphysik, Kühlungsborn, March 22, 2019.

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

V. John, Algebraic finite element stabilizations for convectiondiffusion 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, 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.

A. Linke, On pressurerobustness, coherent structures and vortexdominated flows, Leibniz MMS Days 2019, March 20  22, 2019, Universität Rostock , LeibnizInstitut für Atmosphärenphysik, Kühlungsborn, March 22, 2019.

CH. Merdon, n.n., GeorgAugustUniversität Göttingen, Institut für Numerische und Angewandte Mathematik, January 29, 2019.

P. Vágner, A detailed double layer model of solid oxide cell electrolyteelectrode 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 gasstirred 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 GaussFermi statistics, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), Berlin, October 8  10, 2018.

R. Müller, J. Fuhrmann, C. Guhlke, B. Matejczyk , Dimension reduction of improved NernstPlanck models for charged nanopores, Asymptotic Behavior of systems of PDE arising in physics and biology: theoretical and numerical points of view (ABPDE III), 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), Belgium, May 7  9, 2018.

C. Cancès, C. ChainaisHillairet, J. Fuhrmann, B. Gaudeul, Numerical schemes for a reduced case of an improved NernstPlanckPoisson model, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), Berlin, October 8  10, 2018.

P. Farrell, D. Peschka, Challenges for driftdiffusion simulations of semiconductors: A comparative study of different discretization philosophies, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), 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, WeierstraßInstitut, 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, QuaidiAzam University, Department of Mathematics, Islamabad, Pakistan, November 29, 2018.

C. Bartsch, V. John, R.I.A. Patterson, A new mixed stochasticdeterministic simulation approach to particle populations in fluid flows, 6th International Conference on Population Balance Modelling (PBM2018), 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 penaltyfree 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, LeibnizInstitut für Angewandte Geophysik, Hannover, November 7, 2018.

A. Caiazzo, Multiscale and reducedorder modeling of biphasic materials with application to tissue elastography, Rheinische FriedrichWilhelmsUniversität Bonn, Institut für Numerische Simulation, November 23, 2018.

A. Caiazzo, Multiscale modeling of individualbased cancer models with arbitrary vasculature and fiber structure, ECCMECFD 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) bloodflow simulations, University of Amsterdam, Computational Science Lab, Netherlands, September 21, 2018.

W. Dreyer, NonNewtonian 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 nonNewtonian 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), Berlin, October 8  10, 2018.

J. Fuhrmann, Computational assessment of the derivation of the ButlerVolmer kinetics as a limit case of the NernstPlanck equations with surface reactions, Workshop ``Numerical Optimization of the PEM Fuel Cell Bipolar Plate'', Zentrum für Solarenergie und WasserstoffForschung, 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, Prag, 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 stochasticdeterministic 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, MartinLutherUniversität Halle, Fachbereich Mathematik, October 27, 2018.

V. John, Finite elements for scalar convectiondominated 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 highorder pressurerobust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond, 13th International Workshop on Variational Multiscale and Stabilized Finite Elemements, WeierstraßInstitut, Berlin, December 5, 2018.

A. Linke, On the role of the HelmholtzHodge projector for a novel pressurerobust discretization theory for the incompressible NavierStokes equations, The University of Texas at Austin, Institute for Computational Engineering and Scienses, USA, September 18, 2018.

A. Linke, On the role of the HelmholtzLeray projector for a novel pressurerobust discretization theory for the incompressible NavierStokes 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 HelmholtzLeray projector for a novel pressurerobust discretization theory for the incompressible NavierStokes equations, GeorgAugustUniversität Göttingen, Institut für Numerische und Angewandte Mathematik, January 23, 2018.

A. Linke, On the role of the HelmholtzLeray projector for a novel pressurerobust discretization theory for the incompressible NavierStokes equations, Aix Marseille Université, Institut de Mathématiques, France, April 3, 2018.

A. Linke, On the role of the HelmholtzLeray projector for a novel pressurerobust discretization theory for the incompressible NavierStokes equations, Clemson University, Department of Mathematical Sciences, South Carolina, USA, August 17, 2018.

A. Linke, On the role of the HelmholtzLeray projector in the space discretization of the NavierStokes equations, 3rd Leibniz MMS Days 2018, February 28  March 2, 2018, Wissenschaftszentrum Leipzig, March 1, 2018.

A. Linke, Towards pressurerobust mixed methods for the incompressible NavierStokes 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: Pressurerobust space discretization for the incompressible NavierStokes equations, 2nd NGSolve User Meeting, July 4  6, 2018, GeorgAugustUniversität Göttingen, Institut für Numerische und Angewandte Mathematik, July 5, 2018.

CH. Merdon, Wellbalanced discretisation of the compressible Stokes problem, 13th International Workshop on Variational Multiscale and Stabilized Finite Elemements, WeierstraßInstitut, 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 (ICCMCAM), ShingTung Yau Center of Southeast University, Nanjing, China, December 13, 2018.

H. Si, An algorithm to triangulate 3D nonconvex 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 nonequilibrium irreversible electromagnetothermodynamics 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, SintMichielsgestel, Netherlands, July 4, 2018.

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

U. Wilbrandt, Iterative subdomain methods for the StokesDarcy coupling, ECCMECFD 2018, June 11  15, 2018, University of Glasgow, UK, June 11, 2018.
External Preprints

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 pp. 15, Cornell University, 2019.

N. Alia, V. John, S. Ollila, Revisiting the singlephase 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 singlephase flow models. It aims at improving the existing models from the literature. Simulations in a 2d axialsymmetrical configuration, as well as, in a real 3d laboratoryscale 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 highorder pressurerobust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond, Preprint, Cornell University Library, 2018.
Abstract
Recently, highorder space discretisations were proposed for the numerical simulation of the incompressible NavierStokes 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 highorder space discretisations is more robust against quantitatively large and complicated pressure fields than loworder methods. Second, it is demonstrated that novel pressurerobust methods are significantly more accurate than comparable classical, nonpressurerobust space discretisations, whenever the quadratic, nonlinear convection term is a nontrivial gradient field like in certain generalised Beltrami flows at high Reynolds number. Then, pressurerobust methods even allow to halve the (formal) approximation order without compromising the accuracy. Third, classical highorder space discretisations are outperformed by pressurerobust methods whenever the boundary is not approximated with highorder accuracy. This improved accuracy of (loworder) pressurerobust mixed methods is explained in terms of a HelmholtzHodge 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 pressurerobust and classical space discretisations. Further, the relevance of these results is discussed for flows that are not of Beltrami type.
Research Groups
 Partial Differential Equations
 Laser Dynamics
 Numerical Mathematics and Scientific Computing
 Nonlinear Optimization and Inverse Problems
 Interacting Random Systems
 Stochastic Algorithms and Nonparametric Statistics
 Thermodynamic Modeling and Analysis of Phase Transitions
 Nonsmooth Variational Problems and Operator Equations