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: 


+49-30-2044975

google scholar: 


link



Contents

Research Interests

  • Numerical mathematics

  • Incompressible Navier-Stokes equations

  • Reaction-advection-diffusion equations

  • Finite Elements

  • Finite Volumes

In my research, I try to find discretizations for partial differential equations (PDE) which preserve fundamental qualitative properties of the PDEs in the discretizations, like:

  • Local and global mass conservation

  • Maximum principles and positivity

I believe that the preservation of qualitative properties is of central importance in many discretizations for multi physics problems.

Refereed Journal Contributions

Title / Author Year
21.) Guaranteed energy error estimators for a modified robust Crouzeix-Raviart Stokes element.
A. Linke, C. Merdon
Journal of Scientific Computing, accepted
2014
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

24.) Robust arbitrary order mixed finite element methods for the incompressible Stokes equations.
A. Linke, G. Matthies, L. Tobiska
2014
23.) 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
2014
22.) Convergence of an implicit Voronoi finite volume method for reaction-diffusion problems.
A. Fiebach, A. Glitzky, A. Linke
2014
21.) Improving efficiency of coupled schemes for Navier-Stokes equations by a connection to grad-div stabilized projection methods.
A. Linke, M. Neilan, L. Rebholz, N. Wilson
2013

PhD Thesis

Proceedings

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

Preprints & Technical Reports

Robust arbitrary order mixed finite element methods for the incompressible Stokes equations.
A. Linke, G. Matthies, L. Tobiska
WIAS Preprint 2027
2014
Guaranteed energy error estimators for a modified robust Crouzeix-Raviart Stokes element.
A. Linke, C. Merdon
WIAS Preprint 1979
2014
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
WIAS Preprint 1929
2014
Improving efficiency of coupled schemes for Navier-Stokes equations by a connection to grad-div stabilized projection methods.
A. Linke, M. Neilan, L. Rebholz, N. Wilson
WIAS Preprint 1835
2013
Convergence of an implicit Voronoi finite volume method for reaction-diffusion problems.
A. Fiebach, A. Glitzky, A. Linke
WIAS Preprint 1827
2013
On the Role of the Helmholtz-Decomposition in Mixed Methods for Incompressible Flows and a New Variational Crime.
A. Linke
WIAS Preprint 1810
2013
On a reduced sparsity stabilization of grad-div type for incompressible flow problems.
A. Linke, L. Rebholz
Matheon Preprint 1003
2013
On the parameter choice in grad-div stabilization for incompressible flow problems.
E. Jenkins, V. John, A. Linke, L. Rebholz
WIAS Preprint 1751
2012
A divergence-free velocity reconstruction for incompressible flows.
A. Linke
Matheon Preprint 986
2012
On incompressible flow simulations using Scott-Vogelius finite elements.
B. Cousins, S. Le Borne, A. Linke, L. Rebholz, Z. Wang
Matheon Preprint 983
2012
Uniform global bounds for solutions of an implicit Voronoi finite volume method for reaction-diffusion problems.
A. Fiebach, A. Glitzky, A. Linke
WIAS Preprint 1718
2012
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
WIAS Preprint 1671
2011
MAC schemes on triangular Delaunay meshes.
R. Eymard, J. Fuhrmann, A. Linke
WIAS Preprint 1654
2011
An assessment of discretizations for convection-dominated convection-diffusion equations.
M. Augustin, A. Caiazzo, A. Fiebach, J. Fuhrmann, V. John, A. Linke, R. Umla
WIAS Preprint 1609
2011
On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius solutions for incompressible flow problems.
A. Linke, L. Rebholz, N. Wilson
WIAS Preprint 1589
2011
A numerical method for mass conservative coupling between fluid flow and solute transport.
J. Fuhrmann, H. Langmach, A. Linke
WIAS Preprint 1521
2010
New connections between finite element formulations of the Navier-Stokes equations.
A. Bowers, B. Cousins, A. Linke, L. Rebholz
WIAS Preprint 1516
2010
Improving mass conservation in FE approximations of the Navier Stokes equations using continuous velocity fields: A connection between grad-div stabilization and Scott-Vogelius elements.
M. Case, V. Ervin, A. Linke, L. Rebholz
WIAS Preprint 1510
2010
Stable computing with an enhanced physics based scheme for the 3d Navier-Stokes equations.
M. Case, V. Ervin, A. Linke, L. Rebholz, N. Wilson
WIAS Preprint 1509
2010
Convergence of a finite volume scheme for the biharmonic problem.
R. Eymard, Th. Gallouët, R. Herbin, A. Linke
WIAS Preprint 1482
2010
A model of an electrochemical flow cell with porous layer.
M. Ehrhardt, J. Fuhrmann, A. Linke
WIAS Preprint 1437
2009
Collision in a cross-shaped domain - A steady 2d Navier-Stokes example demonstrating the importance of mass conservation in CFD.
A. Linke
WIAS Preprint 1408
2009
Mathematical Modeling of Channel-Porous Layer Interfaces in PEM Fuel Cells.
M. Ehrhardt, J. Fuhrmann, A. Linke, E. Holzbecher
WIAS Preprint 1375
2008
Non-nested multi-grid solvers for mixed divergence-free Scott-Vogelius discretizations.
A. Linke, G. Matthies, L. Tobiska
WIAS Preprint 1261
2007
Stabilized finite element schemes for incompressible flow using Scott-Vogelius elements.
E. Burman, A. Linke
WIAS Preprint 1165
2006
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

Lectures

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