PD Dr. Alexander Linke

Address

Weierstrass Institute for Applied Analysis and Stochastics
Mohrenstr. 39
10117 Berlin
Germany

e-mail:


alexander.linke[at]wias-berlin.de

phone:


+49-30-20372-463

fax: 


+49-30-20372-317

google scholar: 


link



Contents

Research Interests

  • Numerical analysis for partial differential equations (PDEs)

  • Incompressible Navier-Stokes equations & reaction-advection-diffusion equations

  • Finite Elements, Finite Volumes & Discontinuous Galerkin Methods

In my research, I try to find robust discretizations for PDEs, which preserve fundamental qualitative properties of the continuous problem, like:

  • Pressure-robust mixed methods for the incompressible Navier-Stokes equations (velocity error is independent of the pressure)

  • Discrete L-bounds, discrete maximum principles, and discrete positivity

I believe that the preservation of qualitative properties is of central importance for the robust discretization of multi physics problems.

Refereed Journal Contributions

Title / Author Year
44.) On the numerical range of sectorial forms.
A. F. M. ter Elst, A. Linke, J. Rehberg
Pure and Applied Functional Analysis, accepted
2020
43.) A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem.
M. Akbas, Th. Gallouet, A.Gassmann, A.Linke, C.Merdon
Computer Methods in Applied Mechanics and Engineering, Vol. 367
2020
42.) Pressure-robustness in quasi-optimal a priori estimates for the Stokes problem.
A. Linke, C. Merdon, M. Neilan
ETNA, Vol. 52, pp. 281-294
2020
41.) On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond.
N. Gauger, A. Linke, P. Schroeder
SMAI Journal of Computational Mathematics, Vol. 5, pp. 89-129
2019
40.) Induced charge electroosmotic flow with finite ion size and solvation effects.
J. Fuhrmann, C. Guhlke, A. Linke, C. Merdon, R. Müller
Electrochimica Acta, Vol. 317, pp. 778-785
2019
39.) Pressure-induced locking in mixed methods for time-dependent (Navier-)Stokes equations.
A. Linke, L. Rebholz
Journal of Computational Physics, Vol. 388, pp. 350-356
2019
38.) Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier-Stokes equations.
C. Lehrenfeld, A. Linke, G. Lube, P. Schroeder
SeMA Journal, Vol. 75(4), pp. 629-653
2018
37.) The analogue of grad–div stabilization in DG methods for incompressible flows: Limiting behavior and extension to tensor-product meshes.
M. Akbas, A. Linke, L. Rebholz, P. Schroeder
Computer Methods in Applied Mechanics and Engineering, Vol. 341(1), pp. 917-938
2018
36.) Towards pressure-robust mixed methods for the incompressible Navier-Stokes equations.
N. Ahmed, A. Linke, C. Merdon
Computational Methods in Applied Mathematics, Vol. 18(3), pp. 353-372
2018
35.) Quasi-optimality of a pressure-robust nonconforming finite element method for the Stokes-Problem.
A. Linke, C. Merdon, M. Neilan, F. Neumann
Mathematics of Computation, Vol. 87, pp. 1543-1566
2018
34.) On Really Locking-Free Mixed Finite Element Methods for the Transient Incompressible Stokes Equations.
N. Ahmed, A. Linke, C. Merdon
SIAM Journal on Numerical Analysis, Vol. 56(1), 185-209
2018
33.) A connection between coupled and penalty projection timestepping schemes with FE spatial discretization for the Navier-Stokes equations.
A. Linke, M. Neilan, L. Rebholz, N. Wilson
Journal of Numerical Mathematics, Vol. 25(4), 229-248
2017
32.) On the divergence constraint in mixed finite element methods for incompressible flows.
V. John, A. Linke, C. Merdon, M. Neilan, L. Rebholz
SIAM Review, Vol. 59(3), pp. 492-544
2017
31.) Uniform second order convergence of a complete flux scheme on unstructured 1D grids for a singularly perturbed advection-diffusion equation and some multidimensional extensions.
P. Farrell, A. Linke
Journal of Scientific Computing, Vol. 72(1), pp. 373-395
2017
30.) Divergence-free Reconstruction Operators for Pressure-Robust Stokes Discretizations With Continuous Pressure Finite Elements.
P. Lederer, A. Linke, C. Merdon, J. Schöberl
SIAM Journal on Numerical Analysis, Vol. 55(3), pp. 1291-1314
2017
29.) Optimal L2 velocity error estimate for a modified pressure-robust Crouzeix-Raviart Stokes element.
A. Linke, C. Merdon, W. Wollner
IMA Journal of Numerical Analysis, Vol. 37(1), pp. 354-374
2017
28.) Pressure-robustness and discrete Helmholtz projectors in mixed finite element methods for the incompressible Navier-Stokes equations.
A. Linke, C. Merdon
Computer Methods in Applied Mechanics and Engineering, Vol. 311, pp. 304-326
2016
27.) Inverse modeling of thin layer flow cells for detection of solubility, transport and reaction coefficients from experimental data.
J. Fuhrmann, A. Linke, C. Merdon, F. Neumann, T. Streckenbach, H. Baltruschat, M. Khodayari
Electrochimica Acta, Vol. 211, pp. 1-10
2016
26.) A discontinuous skeletal method for the viscosity-dependent Stokes problem.
D. di Pietro, A. Ern, A. Linke, F. Schieweck
Computer Methods in Applied Mechanics and Engineering, Vol. 306, pp. 175-195
2016
25.) On velocity errors due to irrotational forces in the Navier-Stokes momentum balance.
A. Linke, C. Merdon
Journal of Computational Physics, Vol. 313, pp. 654-661
2016
24.) Robust arbitrary order mixed finite element methods for the incompressible Stokes equations with pressure independent velocity errors.
A. Linke, G. Matthies, L. Tobiska
ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 50(1), pp. 289-309
2016
23.) Convergence of an implicit Voronoi finite volume method for reaction-diffusion problems.
A. Fiebach, A. Glitzky, A. Linke
Numerical Methods for Partial Differential Equations, Vol. 32(1), pp. 141-174
2016
22.) Guaranteed energy error estimators for a modified robust Crouzeix-Raviart Stokes element.
A. Linke, C. Merdon
Journal of Scientific Computing, Vol. 64(2), pp. 541-558
2015
21.) Optimal and pressure-independent L2 velocity error estimates for a modified Crouzeix-Raviart Stokes element with BDM reconstructions.
C. Brennecke, A. Linke, C. Merdon, J. Schöberl
Journal of Computational Mathematics, Vol. 33(2), pp. 191-208
2015
20.) Uniform global bounds for solutions of an implicit Voronoi finite volume method for reaction-diffusion problems.
A. Fiebach, A. Glitzky, A. Linke
Numerische Mathematik, Vol. 128(1), pp. 31-72
2014
19.) On MAC Schemes on Triangular Delaunay Meshes, their Convergence and Application to Coupled Flow Problems.
R. Eymard, J. Fuhrmann, A. Linke
Numerical Methods for Partial Differential Equations, Vol. 30(4), pp. 1397–1424
2014
18.) On the parameter choice in grad-div stabilization for incompressible flow problems.
E. Jenkins, V. John, A. Linke, L. Rebholz
Advances in Computational Mathematics, Vol. 40(2), pp. 491-516
2014
17.) On the Role of the Helmholtz-Decomposition in Mixed Methods for Incompressible Flows and a New Variational Crime.
A. Linke
Computer Methods in Applied Mechanics and Engineering, Vol. 268, pp. 782-800
2014
16.) On a reduced sparsity stabilization of grad–div type for incompressible flow problems.
A. Linke, L. Rebholz
Computer Methods in Applied Mechanics and Engineering, Vol. 261–262, pp. 142-153
2013
15.) Efficient linear solvers for incompressible flow simulations using Scott-Vogelius finite elements.
B. Cousins, S. Le Borne, A. Linke, L. Rebholz, Z. Wang
Numerical Methods for Partial Differential Equations, Vol. 29(4), pp. 1217-1237
2013
14.) A divergence-free velocity reconstruction for incompressible flows.
A. Linke
Comptes Rendus Mathematique, Vol. 350 (17-18), pp. 837-840
2012
13.) Finite volume schemes for the biharmonic problem on general meshes.
R. Eymard, Th. Gallouët, R. Herbin, A. Linke
Mathematics of Computation, Vol. 81 (280), pp. 2019–2048
2012
12.) Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection.
K. Galvin, A. Linke, L. Rebholz, N. Wilson
Computer Methods in Applied Mechanics and Engineering, Vol. 237-240, pp. 166-176
2012
11.) An assessment of discretizations for convection-dominated convection-diffusion equations.
M. Augustin, A. Caiazzo, A. Fiebach, J. Fuhrmann, V. John, A. Linke, R. Umla
Computer Methods in Applied Mechanics and Engineering, Vol. 200 (47-48), pp. 3395–3409
2011
10.) A Connection Between Scott–Vogelius and Grad-Div Stabilized Taylor–Hood FE Approximations of the Navier–Stokes Equations.
M. Case, V. Ervin, A. Linke, L. Rebholz
SIAM Journal on Numerical Analysis, Vol. 49(4), pp. 1461-1481
2011
9.) On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius solutions for incompressible flow problems.
A. Linke, L. Rebholz, N. Wilson
Journal of Mathematical Analysis and Applications, Vol. 381, pp. 612-626
2011
8.) A numerical method for mass conservative coupling between fluid flow and solute transport.
J. Fuhrmann, H. Langmach, A. Linke
Applied Numerical Mathematics, Vol. 61(4), pp. 530-553
2011
7.) Stable computing with an enhanced physics based scheme for the 3d Navier-Stokes equations.
M. Case, V. Ervin, A. Linke, L. Rebholz, N. Wilson
International Journal of Numerical Analysis and Modeling, Vol. 8(1), pp. 118-136
2011
6.) New connections between finite element formulations of the Navier-Stokes equations.
A. Bowers, B. Cousins, A. Linke, L. Rebholz
Journal of Computational Physics, Vol. 229 (24), pp. 9020-9025
2010
5.) Advanced Expression Templates Programming.
J. Härdtlein, C. Pflaum, A. Linke, H. Wolters
Computing and Visualization in Science, Vol. 13 (2), pp. 59-68
2010
4.) Numerical calculation of the limiting current for a cylindrical thin layer flow cell.
J. Fuhrmann, A. Linke, H. Langmach, H. Baltruschat
Electrochimica Acta, Vol. 55 (2), pp. 430-438
2009
3.) Collision in a cross-shaped domain - A steady 2d Navier-Stokes example demonstrating the importance of mass conservation in CFD.
A. Linke
Computer Methods in Applied Mechanics and Engineering, Vol. 198 (41-44), pp. 3278-3286
2009
2.) Non-nested multi-grid solvers for mixed divergence-free Scott-Vogelius discretizations.
A. Linke, G. Matthies, L. Tobiska
Computing, Vol. 83 (2-3), pp. 87-107
2008
1.) Stabilized finite element schemes for incompressible flow using Scott-Vogelius elements.
E. Burman, A. Linke
Applied Numerical Mathematics, Vol. 58 (11),  pp. 1704-1719
2008

Submitted Manuscripts

47.) A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation.
N. Ahmed, G. Barrenechea, E. Burman, J. Guzmán, A. Linke, C. Merdon
2020
46.) A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes.
T. Apel, V. Kempf, A. Linke, C. Merdon
2020
45.) Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity.
G. Fu, C. Lehrenfeld, A. Linke, T. Streckenbach
2020

Habilitation Thesis

Towards Pressure-robust Discretizations for the Incompressible Navier-Stokes Equation. Free University of Berlin, Department Mathematics and Computer Science.
A. Linke
2018

PhD Thesis

Proceedings

Models and numerical methods for electrolyte flows.
J. Fuhrmann, C. Guhlke, A. Linke, C. Merdon, R. Müller
Topics in Applied Analysis and Optimisation, Springer International Publishing, CIM Series in Mathematical Sciences, pp. 183-209, 2019, ISBN 978-3-030-33115-3
Voronoi Finite Volumes and Pressure Robust Finite Elements for Electrolyte Models with Finite Ion Sizes.
J. Fuhrmann, C. Guhlke, A. Linke, C. Merdon, R. Müller
Numerical Geometry, Grid Generation and Scientific Computing. Springer, Lecture Notes in Computational Science and Engineering book series Vol. 131, pp. 73-83, 2019, ISBN 978-3-030-23435-5
Nonlinear flux approximation scheme for Burgers equation derived from a local BVP.
J.H.M. ten Thije Boonkkamp, N. Kumar, B. Koren, D.A.M. van der Woude, A. Linke
ENUMATH, European Conference on Numerical Mathematics and Advanced Applications, Voss, September 25-29, 2017. Springer, Lecture Notes in Computational Science and Engineering, Vol. 126, pp. 1015-1023, 2019, ISBN 978-3-319-96414-0
Towards Pressure-Robust Mixed Methods for the Incompressible Navier-Stokes Equations.
N. Ahmed, A. Linke, C. Merdon
FVCA 8, Finite Volumes for Complex Applications VIII, Lille, June 12-16, 2017, Springer Proceedings in Mathematics & Statistics, pp. 351-359, ISBN-978-3-319-57396-0
Uniform Second Order Convergence of a Complete Flux Scheme on Nonuniform 1D Grids.
P. Farrell, A. Linke
FVCA 8, Finite Volumes for Complex Applications VIII, Lille, June 12-16, 2017, Springer Proceedings in Mathematics & Statistics, pp. 303-310, ISBN-978-3-319-57396-0
A Nonlinear Flux Approximation Scheme for the Viscous Burgers Equation.
N. Kumar, J. H. M. ten Thije Boonkkamp, B. Koren, A. Linke
FVCA 8, Finite Volumes for Complex Applications VIII, Lille, June 12-16, 2017, Springer Proceedings in Mathematics & Statistics, pp. 457-465, ISBN-978-3-3-57393-9
Coupling of Fluid Flow and Solute Transport Using a Divergence-Free Reconstruction of the Crouzeix-Raviart Element.
J. Fuhrmann, A. Linke, C. Merdon
FVCA 7, Finite Volumes for Complex Applications VII, Berlin, June 15-20, 2014, Springer Proceedings in Mathematics & Statistics, pp. 587-595, ISBN-978-3-319-05590-9
Optimal and pressure-independent L2 velocity error estimates for a modified Crouzeix-Raviart Stokes element with BDM reconstructions.
C. Brennecke, A. Linke, C. Merdon, J. Schöberl
FVCA 7, Finite Volumes for Complex Applications VII, Berlin, June 15-20, 2014, Springer Proceedings in Mathematics & Statistics, pp. 159-167, ISBN-978-3-319-05683-8
Mass Conservative Coupling Between Fluid Flow and Solute Transport.
J. Fuhrmann, A. Linke, H. Langmach
FVCA 6, Finite Volumes for Complex Applications VI, Prague, June 6-10, 2011, Springer Proceedings in Mathematics 4, pp. 475-483, ISBN-978-3-642-20670-2
MAC Schemes on Triangular Meshes.
R. Eymard, J. Fuhrmann, A. Linke
FVCA 6, Finite Volumes for Complex Applications VI, Prague, June 6-10, 2011, Springer Proceedings in Mathematics 4, pp. 399-407, ISBN-978-3-642-20670-2
Mathematical Modeling of Channel-Porous Layer Interfaces in PEM Fuel Cells.
M. Ehrhardt, J. Fuhrmann, A. Linke, E. Holzbecher
FDFC 2008, Conference on Fundamentals and Developments of Fuel Cells, University of Nancy, 10-12th December, 2008, Nancy, France, ISBN 978-2-7466-0413-1
Fast Expression Templates - Object Oriented High Performance Programming.
J. Härdtlein, A. Linke, C. Pflaum
LNCS Vol. 3515, pp. 1055-1063, Springer 2005
Scientific Progress in the Par-EXPDE-Project.
A. Linke, C. Pflaum, B. Bergen
In: S. Wagner, W. Hanke,  A. Bode, F. Durst Performance Computing in Science and Engineering, Munich 2002 (First Joint HLRB and KONWIHR Status and Result Workshop, München, 10.-11. Oktober 2002) . Berlin, Springer, 2003, pp. 483-492, ISBN 3-540-00474-2

Some Preprints & Technical Reports

A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation.
N. Ahmed, G. Barrenechea, E. Burman, J. Guzmán, A. Linke, C. Merdon
arXiv:2007.04012
2020
A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes.
T. Apel, V. Kempf, A. Linke, C. Merdon
arXiv:2002.12127
2020
Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity.
G. Fu, C. Lehrenfeld, A. Linke, T. Streckenbach
arXiv:2001.08610
2020
On the numerical range of sectorial forms.
A. ter Elst, A. Linke, J. Rehberg
arXiv:1912.09169
2019
A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem.
M. Akbas, Th. Gallouet, A. Gassmann, A. Linke, C. Merdon
arXiv:1911.01295
2019
Blocking Techniques with Fast Expression Templates.
J. Härdtlein, A. Linke, C. Pflaum
Computer Science 10, University of Erlangen. Technical Report 06-8
2006
Fast Expression Templates - Enhancements for High Performance C++ Libraries.
J. Härdtlein, A. Linke, C. Pflaum
Computer Science 10, University of Erlangen. Technical Report 06-7
2006
Fast Expression Templates for the Hitachi SR8000 Supercomputer.
A. Linke, C. Pflaum
Computer Science 10, University of Erlangen. Technical Report 03-9
2003

Awards

J. Tinsley Oden Faculty Fellowship, September 2018
ICES, University of Texas at Austin
2018

Invited Plenary Talks at International Conferences

Structure, Regularity, and Robustness in the Approximation of Partial Differential Equations (February 10, 2020).
Università degli Studi di Milano
2020
POEMS – POlytopal Element Methods in Mathematics and Engineering (April 29-May 3, 2019).
CIRM, Marseille
2019
CASM International Conference on Applied Mathematics (May 22-24, 2017).
LUMS, Lahore
2017
IHP Quarter on Numerical Methods for PDEs: (ME2) Conference: Advanced numerical methods: recent developments, analysis, and applications (October 3-7, 2016).
IHP, Paris (keynote lecture)
2016
CDZ Workshop Modelling, Model Reduction, and Optimization of Flows (September 25-29, 2016).
Shanghai University, Shanghai
2016
Workshop on Nonlinear PDEs & Applications (May 5-7, 2014).
Tanger (keynote lecture)
2014

Lectures

Analysis I (Mathematik für Physiker I)
A. Linke
Free University Berlin, Summer semester 2018
Ba Optinum: Optimierung und Numerik
A. Linke
Technical University Dresden, Summer semester 2015
Ma PDENMW: Numerik mit partiellen Differentialgleichungen
A. Linke
Technical University Dresden, Summer semester 2015
Mathematik für Physiker I
A. Linke
Free University Berlin, Winter semester 2011/2012
Simulation inkompressibler Strömungen (Numerische Mathematik IVb)
Prof. V. John, A. Linke
Free University Berlin, Winter semester 2010/2011

Master Students Completed

Bachelor Students Completed