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Article

Gelß, P. and Issagali, A. and Kornhuber, R. (2023) Fredholm integral equations for function approximation and the training of neural networks. arXiv . (Submitted)

Kornhuber, R. and Podlesny, J. and Yserentant, H. (2022) Numerical homogenization of fractal interface problems. ESAIM: M2AN, 56 (4). 1451- 1481. ISSN 2822-7840 - eISSN: 2804-7214

Heida, M. and Kornhuber, R. and Podlesny, J. (2020) Fractal homogenization of multiscale interface problems. Multiscale Modeling & Simulation, 18 (1). pp. 294-314. ISSN 1540-3459

Kies, T. and Gräser, C. and Delle Site, L. and Kornhuber, R. (2020) Free energy computation of particles with membrane-mediated interactions via Langevin dynamics. arXiv:2009.14713 . pp. 1-20. (Submitted)

Rosenau, M. and Horenko, I. and Corbi, F. and Rudolf, M. and Kornhuber, R. and Oncken, O. (2019) Synchronization of great subduction megathrust earthquakes: Insights from scale model analysis. Journal of Geophysical Research: Solid Earth, 124 (4). pp. 3646-3661. ISSN 2169-9356

Youett, J. and Sander, O. and Kornhuber, R. (2019) A globally convergent filter-trust-region method for large deformation contact problems. SIAM J. Sci. Comput., 41 (1). B114-B138. ISSN 1064-8275

Djurdjevac, A. and Elliott, C.M. and Kornhuber, R. and Ranner, Th. (2018) Evolving surface finite element methods for random advection-diffusion equations. SIAM/ASA Journal on Uncertainty Quantification, 6 (4). pp. 1656-1684. ISSN 2166-2525

Kornhuber, R. and Youett, E. (2018) Adaptive Multilevel Monte Carlo Methods for Stochastic Variational Inequalities. SIAM Journal on Numerical Analysis, 56 (4). pp. 1987-2007. ISSN 0036-1429

Kornhuber, R. and Peterseim, D. and Yserentant, H. (2018) An analysis of a class of variational multiscale methods based on subspace decomposition. Mathematics of Computation, 87 (314). pp. 2765-2774. ISSN 1088-6842 (online)

Kornhuber, R. and Yserentant, H. (2016) Numerical Homogenization of Elliptic Multiscale Problems by Subspace Decomposition. Multiscale Model. Simul., 14 (3). pp. 1017-1036. ISSN print: 1540-3459; online: 1540-3467

Gräser, C. and Kahnt, M. and Kornhuber, R. (2016) Numerical approximation of multi-phase Penrose-Fife systems. Computational Methods in Applied Mathematics, 16 (4). pp. 523-542. ISSN Online: 1609-9389, Print: 1609-4840

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, 222 (2). pp. 1011-1075. ISSN Print: 0003-9527; Online:1432-0673

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

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

Gräser, C. and Kornhuber, R. and Sack, U. (2014) Numerical simulation of coarsening in binary solder alloys. Computational Materials Science, 93 . pp. 221-233. ISSN 0927-0256

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

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

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

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

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

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

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

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

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

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.

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

Deuflhard, P. and Ertel, S. and Kornhuber, R. and Krause, R. and Sander, O. (2006) Patient-specific simulation of dynamic stress distribution in the human knee. Journal of Biomechanics, 39 . p. 47. ISSN 0021-9290

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

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. (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

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

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

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

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

Roitzsch, R. and Kornhuber, R. (1990) BOXES - a program to generate triangulations from a rectangular domain description. ZIB-Report, TR-90- . ISSN 1438-0064

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

Kornhuber, R. and Roitzsch, R. (1989) Adaptive Finite-Element-Methoden für konvektionsdominierte Randwertprobleme bei partiellen Differentialgleichungen. ZIB-Report . ISSN 1438-0064

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

Kornhuber, R. (1973) Vereinfachung eines Computermodells. MNU - Der mathematische und naturwissenschaftliche Unterricht, 26 (3). p. 176. ISSN 0025-5866

Book Section

Kornhuber, R. and Sander, O. and Schiela, A. and Weiser, M. (2021) Wear Testing of Knee Implants. In: German Success Stories in Industrial Mathematics. Springer, pp. 85-90. ISBN Print 978-3-030-81454-0; Online 978-3-030-81455-7

Kornhuber, R. and Podlesny, J. and Yserentant, H. (2017) Direct and Iterative Methods for Numerical Homogenization. In: Domain Decomposition Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, XXIII (116). SpringerLink, pp. 217-225. ISBN 978-3-319-52389-7

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

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

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

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

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

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

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

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

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. (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

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.

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

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

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

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

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

Kornhuber, R. and Wittum, G. (1993) Discretization and preconditioning of convection diffusion equations. In: Incomplete Decomposition (ILU) - Algorithms, Theory, and Applications. Notes on Numerical Fluid Mechanics (41). Springer Vieweg, pp. 67-77. ISBN 978-3-528-07641-2

Kornhuber, R. and Roitzsch, R. (1991) Self adaptive computation of the breakdown voltage of planar pn-junctions with multistep field plates. In: Proc. 4th International Conference on Simulation of Semiconductor Devices and Processes. Hartung-Gorre Verlag, Zürich, pp. 535-543. ISBN 3-89191-476-8

Hoppe, R. H. W. and Kornhuber, R. (1989) Numerical simulation of induction heating processes by multi-grid techniques. In: Numerical methods in Thermal Problems. Pineridge Press, Swansea, pp. 1142-1152.

Hoppe, R. H. W. and Kornhuber, R. (1988) Multi-grid solution of the two-phase Stefan problem. In: Multigrid Methods: Theory, Applications and Supercomputing. Lecture Notes in Pure and Applied Mathematics (110). Marcel Dekker Inc., pp. 267-297. ISBN 0824779797, 978-0824779795

Conference or Workshop Item

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.

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.

Book

Bjørstad, P. E. and Brenner, S. C. and Halpern, L. and Kim, H. H. and Kornhuber, R. and Rahman, T. and Widlund, O. B., eds. (2018) Domain Decomposition Methods in Science and Engineering XXIV. Lecture Notes in Computational Science and Engineering, 125 . Springer International Publishing. ISBN 978-3-319-93872-1

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, 12 (4). European Mathematical Society - Publishing House, Zürich, Switzerland.

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

Dziuk, G. and Elliott, C.M. and Huisken, G. and Kornhuber, R. (2011) Geometric partial differential equations: Theory, numerics and applications. Oberwolfach Reports, 8 (4). European Mathematical Society.

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

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

Kornhuber, R. (1997) Adaptive monotone multigrid methods for nonlinear variational problems. Advances in Numerical Mathematics . Vieweg+Teubner Verlag, Stuttgart. ISBN 3519027224