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



Announcement

  • FU-Berlin, WS20/21, Vorlesung 19208801 Mathematik für Geowissenschaftler I:
  • Online-Vorlesung via zoom:
  • https://us02web.zoom.us/j/84005388550?pwd=TGlGa0NxM0haVVVLVkdMc1dMYjkyZz09
  • Meeting-ID: 840 0538 8550
  • Kenncode: 670928
  • 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
    46.) Locking free and gradient robust H(div)-conforming HDG methods for linear elasticity.
    G. Fu, C. Lehrenfeld, A. Linke, T. Streckenbach
    Journal of Scientific Computing, accepted
    2020
    45.) A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes.
    T. Apel, V. Kempf, A. Linke, C. Merdon
    IMA Journal on Numerical Analysis, accepted
    2020
    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

    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
    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

    ALGORITMY 2020 (September 10-15).
    Vysoke Tatry, Podbanske
    2020
    Structure, Regularity, and Robustness in the Approximation of Partial Differential Equations (February 10).
    Università degli Studi di Milano
    2020
    POEMS – POlytopal Element Methods in Mathematics and Engineering (April 29-May 3).
    CIRM, Marseille
    2019
    CASM International Conference on Applied Mathematics (May 22-24).
    LUMS, Lahore
    2017
    IHP Quarter on Numerical Methods for PDEs: (ME2) Conference: Advanced numerical methods: recent developments, analysis, and applications (October 3-7).
    IHP, Paris (keynote lecture)
    2016
    CDZ Workshop Modelling, Model Reduction, and Optimization of Flows (September 25-29).
    Shanghai University, Shanghai
    2016
    Workshop on Nonlinear PDEs & Applications (May 5-7).
    Tanger (keynote lecture)
    2014

    Lectures

    Mathematik für Geowissenschaftler I
    A. Linke
    Free University Berlin, Winter semester 2020/21
    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