Prof. Dr. Ralf Kornhuber

Ralf Kornhuber

FU Berlin

FB Mathematik und Informatik

Numerical Analysis of Partial Differential Equations

Professor

Address Arnimallee 6
Room 130
14195 Berlin
Telephone +49 30 838 75350
Fax +49 30 838 475407
Email ralf.kornhuber[at]fu-berlin.de

Office hours

Tuesday, 11-12 a.m.

Short CV:

Full Professor (C4), FU Berlin (since 1998)
Offer Full Professor, University of Düsseldorf, not realized (1997)
Offer Full Professor, University of Leipzig, not realized (1997)
Full Professor (C3), University of Stuttgart (1996-1998)
Head of  research group, WIAS Berlin (1994-1996)
Habilitation in Mathematics, FU Berlin with P. Deuflhard (1995)
Department deputy head, ZIB Berlin (1989-1994)
Research assistant, ZIB Berlin (1987-1989)
Dr. rer. nat  in Mathematics, TU Berlin with R.D. Grigorieff (1986)
Research assistant, TU Berlin (1982-1987)
Software Development Engineer, STS GmbH Berlin (1980-1982)
Diploma in Mathematics, TU Berlin (1979)

Fields of interest:

  • Nonsmooth elliptic and parabolic problems involving multiple scales
  • Variational problems and geometric partial differential equations
  • Subspace correction methods (domain decomposition, multigrid)
  • Adaptive finite element methods and a posteriori error estimation
  • Applications in the geosciences, biomechanics, life sciences, and material sciences

Scientific Boards:

Einstein Center ECMath:  Executive Committee (since 2013)
Einstein Center ECMath:  Deputy Chair (2013 - 2014), Chair (since 2014)
CRC 1114 Scaling Cascades in Complex Systems:  Executive Committee, Deputy Chair (since 2014)
Berlin Mathematical School (BMS): Admission Committee (since 2013)
Int. Scientific Committee of Domain Decomposition Conferences (since 2003),  Chair (2007 - 2013)
Helmholtz Research School GeoSim: Executive Board (since 2011)
Matheon: Executive board (2012 - 2016)

Editorial Boards:

"International Journal of Numerical Analysis and Modeling" (since 2003)
"SIAM Journal on Multiscale Modeling and Simulation (MMS)" (since 2011)
"Computing and Visualization in Science"  (since 2011)

Jump to: 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2003 | 2002 | 2001 | 2000 | 1999 | 1998 | 1997 | 1996 | 1994 | 1993 | 1990 | 1988

Number of items: 70

2016

Kornhuber, R. and Yserentant, H. (2016) An analysis of a class of variational multiscale methods based on subspace decomposition. arXiv:1608.04081 . (Submitted)

Gräser, C. and Kahnt, M. and Kornhuber, R. (2016) Numerical approximation of multi-phase Penrose-Fife systems. MATHEON Preprint number 1103 . (Submitted)

Kornhuber, R. and Podlesny, J. and Yserentant, H. (2016) Direct and Iterative Methods for Numerical Homogenization. SFB 1114 Preprint . (Submitted)

Pipping, E. and Kornhuber, R. and Rosenau, M. and Oncken, O. (2016) On the efficient and reliable numerical solution of rate-and-state friction problems. Geophysical Journal International, 204 (3). pp. 1858-1866. ISSN Online: 1365-246X Print: 0956-540X

Elliott, C.M. and Gräser, C. and Hobbs, G. and Kornhuber, R. and Wolf, M.W. (2016) A Variational Approach to Particles in Lipid Membranes. Archive for Rational Mechanics and Analysis . pp. 1-65. ISSN Print: 0003-9527; Online:1432-0673

2015

Pipping, E. and Sander, O. and Kornhuber, R. (2015) Variational formulation of rate- and state-dependent friction problems. Zeitschrift für angewandte Mathematik und Mechanik (ZAMM), 95 (4). pp. 377-395. ISSN 0044-2267

Berninger, H. and Kornhuber, R. and Sander, O. (2015) A multidomain discretization of the Richards equation in layered soil. Computational Geosciences, 19 (1). pp. 213-232. ISSN 1420-0597

Deckelnick, K. and Elliott, C.M. and Kornhuber, R. and Sethian, J. A., eds. (2015) Geometric partial differential equations: Surface and bulk processes. Oberwolfach Reports (55/2015). European Mathematical Society.

Gräser, C. and Kornhuber, R. and Sack, U. (2015) Nonsmooth Schur-Newton methods for multicomponent Cahn-Hilliard systems. IMA Journal of Numerical Analysis, 35 (2). pp. 652-679. ISSN 0272-4979

Kornhuber, R. and Yserentant, H. (2015) Numerical Homogenization of Elliptic Multiscale Problems by Subspace Decomposition. SFB 1114 Preprint . (Submitted)

2014

Gräser, C. and Kornhuber, R. and Sack, U. (2014) Numerical simulation of coarsening in binary solder alloys. Numerical simulation of coarsening in binary solder alloys, 93 . pp. 221-233. ISSN 09270256

Kornhuber, R. and Schwab, C. and Wolf, M.W. (2014) Multilevel Monte Carlo finite element methods for stochastic elliptic variational inequalities. SIAM Journal on Numerical Analysis, 52 (3). pp. 1243-1268. ISSN 0036-1429

2013

Gräser, C. and Kornhuber, R. and Sack, U. (2013) Time discretizations of anisotropic Allen-Cahn equations. IMA Journal of Numerical Analysis, 33 (4). pp. 1226-1244. ISSN 0272-4979

Sander, O. and Klapproth, C. and Youett, J. and Kornhuber, R. and Deuflhard, P. (2013) Towards an efficient numerical simulation of complex 3D knee joint motion. Computing and Visualization in Science , 16 (3). pp. 119-138. ISSN 1432-9360

Berninger, H. and Kornhuber, R. and Sander, O. (2013) Heterogeneous substructuring methods for coupled surface and subsurface flow. In: Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, 91 . Springer Berlin Heidelberg, pp. 427-434. ISBN 978-3-642-35274-4

Jouvet, G. and Bueler, E. and Gräser, C. and Kornhuber, R. (2013) A nonsmooth Newton multigrid method for a hybrid, shallow model of marine ice sheets. Recent Advances in Scientific Computing and Applications, 586 . pp. 208-217. ISSN 0271-4132

2012

Bastian, P. and Berninger, H. and Dedner, A. and Engwer, C. and Henning, P. and Kornhuber, R. and Kröner, D. and Ohlberger, M. and Sander, O. and Schiffler, G. and Shokina, N. and Smetana, K. (2012) Adaptive modelling of coupled hydrological processes with application in water management. In: Progress in Industrial Mathematics at ECMI 2010. Mathematics in Industry: The European Consortium for Mathematics in Industry (17). Springer Berlin Heidelberg, pp. 561-567. ISBN 978-3-642-25100-9

2011

Berninger, H. and Kornhuber, R. and Sander, O. (2011) Fast and robust numerical solution of the Richards equation in homogeneous soil. SIAM Journal on Numerical Analysis, 49 (6). pp. 2576-2597. ISSN 0036-1429

Berninger, H. and Kornhuber, R. and Sander, O. (2011) Heterogeneous domain decomposition of surface and porous media flow. AIP Conference Proceedings, 1389 . pp. 2025-2028. ISSN 0094-243X

Zou, Q. and Veeser, A. and Kornhuber, R. and Gräser, C. (2011) Hierarchical error estimates for the energy functional in obstacle problems. Numerische Mathematik, 117 (4). pp. 653-677. ISSN 0029-599X

Berninger, H. and Kornhuber, R. and Sander, O. (2011) Convergence behaviour of Dirichlet-Neumann and Robin methods for a nonlinear transmission problem. In: Domain Decomposition Methods in Science and Engineering XIX. Lecture Notes in Computational Science and Engineering, 78 . Springer Berlin Heidelberg, pp. 87-98. ISBN 978-3-642-11303-1

Huang, Y. and Kornhuber, R. and Widlund, O. and Xu, J., eds. (2011) Domain decomposition methods in science and engineering XIX. Lecture Notes in Computational Science and Engineering, 78 . Springer Berlin Heidelberg. ISBN 978-3-642-11303-1

Kornhuber, R. and Zou, Q. (2011) Efficient and reliable hierarchical error estimates for an elliptic obstacle problem. Mathematics of Computation, 80 . pp. 69-88. ISSN 0025-5718

Dziuk, G. and Elliott, C.M. and Huisken, G. and Kornhuber, R. (2011) Geometric partial differential equations: Theory, numerics and applications. Oberwolfach Reports, 4 (54/2011). European Mathematical Society.

2010

Sander, O. and Schmidt, L. and Ehrig, R. and Heller, M. and Taylor, B. and Kornhuber, R. (2010) Numerical determination of the medio-lateral force distribution in an ovine stifle joint. Biomedizinische Technik/Biomedical Engineering: Proceedings of BMT, Rostock, 55 (s1). ISSN 0013-558

Forster, R. and Kornhuber, R. (2010) A polynomial chaos approach to stochastic variational inequalities. Journal of Numerical Mathematics, 18 (4). pp. 235-255. ISSN 1570-2820

Kornhuber, R. (2010) Mathematik hilft heilen. In: Wissenschaftsstadt Berlin. Berliner Wirtschaftsgespräche e.V., p. 123.

Gräser, C. and Kornhuber, R. and Sack, U. (2010) On hierarchical error estimators for time-discretized phase field models. In: Numerical Mathematics and Advanced Applications 2009: Proceedings of ENUMATH 2009. Springer Berlin Heidelberg, pp. 397-405. ISBN 978-3-642-11794-7

2009

Gräser, C. and Sack, U. and Kornhuber, R. (2009) Truncated nonsmooth Newton multigrid methods for convex minimization problems. In: Domain Decomposition Methods in Science and Engineering XVIII. Lecture Notes in Computational Science and Engineering, 70 . Springer Berlin Heidelberg, pp. 129-136. ISBN 978-3-642-02676-8

Gräser, C. and Kornhuber, R. (2009) Nonsmooth Newton methods for set-valued saddle point problems. SIAM Journal on Numerical Analysis, 47 (2). pp. 1251-1273. ISSN 0036-1429

Bercovier, M. and Gander, M. and Kornhuber, R. and Widlund, O., eds. (2009) Domain decomposition methods in science and engineering XVIII. Lecture Notes in Computational Science and Engineering, 70 . Springer Berlin Heidelberg. ISBN 978-3-642-02676-8

Gräser, C. and Kornhuber, R. (2009) Multigrid methods for obstacle problems. Journal of Computational Mathematics, 27 (1). pp. 1-44. ISSN 0254-9409

2008

Kornhuber, R. and Yserentant, H. (2008) Multigrid methods for discrete elliptic problems on triangular surfaces. Computing and Visualization in Science , 11 (4-6). pp. 251-257. ISSN 1432-9360

Bastian, P. and Blatt, M. and Dedner, A. and Engwer, C. and Klöfkorn, R. and Kornhuber, R. and Ohlberger, M. and Sander, O. (2008) A generic grid interface for parallel and adaptive scientific computing. Part II: Implementation and tests in DUNE. Computing, 82 (2-3). pp. 121-138. ISSN 0010-485X

Kornhuber, R. and Krause, R. and Sander, O. and Deuflhard, P. and Ertel, S. (2008) A monotone multigrid solver for two body contact problems in biomechanics. Computing and Visualization in Science , 11 (1). pp. 3-15. ISSN 1432-9360

Forster, R. and Kornhuber, R. and Mautner, R. and Sander, O. (2008) Fast and reliable pricing of American options with local volatility. In: Decomposition Methods in Science and Engineering XVII. Springer, pp. 383-390. ISBN 978-3-540-75198-4

Forster, R. and Kornhuber, R. and Mautner, K. and Sander, O. (2008) Fast and reliable pricing of American options with local volatility. In: Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering , 60 . Springer Berlin Heidelberg, pp. 383-390. ISBN 978-3-540-75198-4

Bastian, P. and Blatt, M. and Dedner, A. and Engwer, C. and Klöfkorn, R. and Kornhuber, R. and Ohlberger, M. and Sander, O. (2008) A generic grid interface for parallel and adaptive scientific computing. II: Implementation and tests in DUNE. Computing, 82 (2-3). pp. 121-138.

2007

Berninger, H. and Kornhuber, R. and Sander, O. (2007) On nonlinear Dirichlet-Neumann Algorithms for jumping nonlinearities. In: Domain Decomposition Methods in Science and Engineering XVI. In: Domain Decomposition Methods in Science and Engineering XVI. LNCSE, 55 . Springer, pp. 489-496. ISBN 978-3-540-34469-8

Kornhuber, R. and Gräser, C. (2007) On preconditioned Uzawa-type iterations for a saddle point problem with inequality constraints. In: Decomposition Methods in Science and Engineering XVI. LNCSE (55). Springer, pp. 91-102. ISBN 978-3-540-34469-8

Gräser, C. and Kornhuber, R. (2007) On preconditioned Uzawa-type iterations for a saddle point problem with inequality constraints. In: Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering , 55 . Springer Berlin Heidelberg, pp. 91-102. ISBN 978-3-540-34468-1

2006

Kornhuber, R. and Krause, R. (2006) Robust multigrid methods for vector-valued Allen-Cahn equations with logarithmic free energy. Computing and Visualization in Science , 9 (2). pp. 103-116. ISSN 1432-9360

Gebauer, S. and Kornhuber, R. and Yserentant, H. (2006) Hierarchical decomposition of domains with fractures. Mathematics of Computation, 75 (253). pp. 73-90. ISSN 00255718

2005

Kornhuber, R. and Hoppe, R. and Périaux, J. and Pironneau, O. and Widlund, O. and Xu, J., eds. (2005) Domain decomposition methods in science and engineering. Lecture Notes in Computational Science and Engineering, 40 . Springer, Berlin. ISBN 978-3-540-22523-2

Schütte, Ch. and Forster, R. and Meerbach, E. and Fischer, A. (2005) Uncoupling-Coupling Techniques for Metastable Dynamical Systems. In: Domain Decomposition Methods in Science and Engineering.

2003

Kornhuber, R. and Krause, R. (2003) On multigrid methods for vector-valued Allen-Cahn equations. In: Proceedings of the fourteenth international conference on domain decomposition methods. National Autonomous University of Mexico (UNAM), Mexico City, Cocoyoc, Mexico, pp. 307-314. ISBN 970-32-0859-2

2002

Ochs, S. and Hinkelmann, R. and Neunhäuserer, L. and Süß, M. and Helmig, R. and Gebauer, S. and Kornhuber, R. (2002) Adaptive methods for the equidimensional modelling of flow and transport processes in fractured aquifers. In: 5th International Conference on Hydroscience and Engineering, ICHE2002, Advances in Hydro-Science and -Engineering., Sept. 17-21, 2002, Warschau.

Gebauer, S. and Neunhäuserer, L. and Kornhuber, R. and Ochs, S. and Hinkelmann, R. and Helmig, R. (2002) Equidimensional modelling of flow and transport processes in fractured porous systems I. In: Computational Methods in Water Resources. Proceedings of the XIVth International Conference on Computational Methods in Water Resources (CMWR XIV). Computational Methods in Water Resources (CMWR XIV), Delft, pp. 335-342. ISBN 978-0-444-50975-8

Neunhäuserer, L. and Gebauer, S. and Ochs, S. and Hinkelmann, R. and Kornhuber, R. and Helmig, R. (2002) Equidimensional modelling of flow and transport processes in fractured porous systems II. In: Computational Methods in Water Resources. Proceedings of the XIVth International Conference on Computational Methods in Water Resources (CMWR XIV). Computational Methods in Water Resources (CMWR XIV), Delft, pp. 343-350. ISBN 978-0-444-50975-8

Kornhuber, R. (2002) On constrained Newton linearization and multigrid for variational inequalities. Numerische Mathematik, 91 (4). pp. 699-721. ISSN 0029-599X

2001

Kornhuber, R. and Krause, R. (2001) Adaptive multigrid methods for Signorini's problem in linear elasticity. Computing and Visualization in Science , 4 (1). pp. 9-20. ISSN 1432-9360

Kornhuber, R. (2001) Nonlinear multigrid techniques. In: Theory and Numerics of Differential Equations. Durham 2000. Universitext . Springer Berlin Heidelberg, pp. 179-229. ISBN 978-3-642-07533-9

2000

Neunhäuserer, L. and Gebauer, S. and Hinkelmann, R. and Kornhuber, R. and Helmig, R. (2000) Mehrgittermethoden und adaptive Diskretisierungsverfahren zur Simulation von Strömungs- und Transportprozessen in Kluftaquiferen. In: 3. Workshop Kluft-Aquifere "Gekoppelte Prozesse in Geosystemen". Institut für Strömungsmechanik und Elektronisches Rechnen im Bauwesen, Hannover, pp. 241-255.

1999

Kornhuber, R. (1999) Monotone iterations for elliptic variational inequalities. In: Free boundary problems: theory and applications. Research notes in mathematics (409). Chapman & Hall/CRC, Boca Raton, London, New York, Washington, D.C., pp. 335-343. ISBN 1-58488-018-X

1998

Kornhuber, R. (1998) On robust multigrid methods for non-smooth variational problems. In: Multigrid methods 5: Proceedings of the Fifth European Multigrid Conference held in Stuttgart, Germany, October 1.4, 1996. Lecture Notes in Computational Science and Engineering (3). Springer Berlin Heidelberg, pp. 173-188. ISBN 978-3-540-63133-0

1997

Kornhuber, R. (1997) Adaptive monotone multigrid methods for some non-smooth optimization problems. In: Domain decomposition methods in science and engineering: 8th international conference, Bejing, P.R. China. John Wiley & Sons, pp. 177-191. ISBN 047196560X

1996

Kornhuber, R. (1996) Monotone multigrid methods for elliptic variational inequalities II. Numerische Mathematik, 72 (4). pp. 481-499. ISSN 0029-599X

Bornemann, F. A. and Erdmann, B. and Kornhuber, R. (1996) A posteriori error estimates for elliptic problems in two and three space dimensions. SIAM Journal on Numerical Analysis, 33 (3). pp. 1188-1204. ISSN 0036-1429

Kornhuber, R. (1996) A posteriori error estimates for elliptic variational inequalities. Computers & Mathematics with Applications, 31 (8). pp. 49-60. ISSN 0898-1221

1994

Erdmann, B. and Hoppe, R. H. W. and Kornhuber, R. (1994) Adaptive multilevel — methods for obstacle problems in three space dimensions. In: Adaptive Methods - Algorithms, Theory and Applications. Notes on Numerical Fluid Mechanics (NNFM), 46 . Vieweg+Teubner Verlag, pp. 120-141. ISBN 978-3-528-07646-7

Hoppe, R. H. W. and Kornhuber, R. (1994) Adaptive multilevel methods for obstacle problems. SIAM Journal on Numerical Analysis, 31 (2). pp. 301-323. ISSN 0036-1429

Kornhuber, R. (1994) Monotone multigrid methods for elliptic variational inequalities I. Numerische Mathematik, 69 (2). pp. 167-184. ISSN 0029-599X

Kornhuber, R. and Yserentant, H. (1994) Multilevel methods for elliptic problems on domains not resolved by the coarse grid. In: Domain Decomposition Methods in Scientific and Engineering Computing. Contemporary Mathematics, 180 . American Mathematical Society, Providence, Rhode Island, pp. 49-60. ISBN 0-8218-5171-3

1993

Bornemann, F. A. and Erdmann, B. and Kornhuber, R. (1993) Adaptive multilevel methods in three space dimensions. International Journal for Numerical Methods in Engineering, 36 (18). pp. 3187-3203. ISSN 1097-0207

Erdmann, B. and Frei, M. and Hoppe, R. H. W. and Kornhuber, R. and Wiest, U. (1993) Adaptive finite element methods for variational inequalities. East-West Journal of Numerical Mathematics, 1 . pp. 165-197. ISSN 1569-3953; 0928-0200

Kornhuber, R. and Roitzsch, R. (1993) Self-adaptive finite-element simulation of bipolar, strongly reverse-biased pn-junctions. International Journal for Numerical Methods in Biomedical Engineering, 9 (3). pp. 243-250. ISSN 2040-7947

1990

Hoppe, R. H. W. and Kornhuber, R. (1990) Multi-grid solution of two coupled Stefan equations arising in induction heating of large steel slabs. International Journal for Numerical Methods in Engineering, 30 (4). pp. 779-801. ISSN 1097-0207

Kornhuber, R. and Roitzsch, R. (1990) On adaptive grid refinement in the presence of internal or boundary layers. IMPACT of Computing in Science and Engineering, 2 (1). pp. 40-72. ISSN 0899-8248

1988

Kornhuber, R. (1988) Convergent extensions of grid-functions. Mathematische Nachrichten, 139 (1). pp. 63-75. ISSN 1522-2616

Kornhuber, R. (1988) Local change of coordinates for grid-functions on regions with curved boundary. Mathematische Nachrichten, 139 (1). pp. 45-61. ISSN 1522-2616