Items where Subject is "Mathematical and Computer Sciences > Mathematics > Numerical Analysis"

Article

Babushkina, E. S. and Bessonov, N. M. and Ataullakhanov, F. I. and Panteleev, M. A. (2015) Continuous modeling of arterial platelet thrombus formation using a spatial adsorption equation. PLoS ONE, 10 (10). ISSN 1932-6203

Banisch, Ralf and Hartmann, C. (2013) Meshless discretization of LQ-type stochastic control problems. arXiv preprint, arXiv: . (Unpublished)

Banisch, Ralf and Hartmann, C. (2016) A sparse Markov chain approximation of LQ-type stochastic control problems. Math. Control Relat. F., 6 (3). pp. 363-389. ISSN 1064-8275

Bastian, P. and Blatt, M. and Dedner, A. and Dreier, N.-A. and Engwer, C. and Fritze, R. and Gräser, C. and Grüninger, C. and Kempf, D. and Klöfkorn, R. and Ohlberger, M. and Sander, O. (2021) The Dune framework: Basic concepts and recent developments. Computers & Mathematics with Applications, 81 . pp. 75-112. ISSN 0898-1221

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

Bastian, P. and Blatt, M. and Dedner, A. and Engwer, C. and Klöfkorn, R. and Ohlberger, M. and Sander, O. (2008) A generic grid interface for parallel and adaptive scientific computing. Part I: Abstract framework. Computing, 82 (2-3). pp. 103-119. ISSN 0010-485X

Bastian, P. and Blatt, M. and Engwer, C. and Dedner, A. and Klöfkorn, R. and Kuttanikkad, S. P. and Ohlberger, M. and Sander, O. (2006) The Distributed and Unified Numerics Environment (DUNE). Proc. of the 19th Symposium on Simulation Technique .

Bernhard, S. (2005) Oscillatory flow in a tube with time-dependent wall deformation and its application to Myocardial Bridges. ESAIM: Proc., 14 . pp. 25-40.

Bernhard, S. (2006) Transient integral boundary layer method to calculate the translesional pressure drop and the fractional flow reserve in myocardial bridges. BioMedical Engineering OnLine, 5 (42).

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

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

Berninger, H. and Loisel, S. and Sander, O. (2014) The 2-Lagrange multiplier method applied to nonlinear transmission problems for the Richards equation in heterogeneous soil with cross points. SIAM J. Sci. Comput., 36 (5). A2166-A2198. ISSN 1064-8275

Berninger, H. and Ohlberger, M. and Sander, O. and Smetana, K. (2014) Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions. Mathematical Models and Methods in Applied Sciences, 24 (5). pp. 901-936. ISSN 1793-6314

Berninger, H. and Sander, O. (2010) Substructuring of a Signorini-type problem and Robin's method for the Richards equation in heterogeneous soil. Computing and Visualization in Science, 13 (5). pp. 187-205. ISSN 1432-9360

Berninger, H. and Werner, Dirk (2003) Lipschitz spaces and M-ideals. Extracta Mathematicae, 18 (1). pp. 33-56. ISSN 0213-8743

Bittracher, Andreas and Koltai, Péter and Junge, Oliver (2015) Pseudogenerators of spatial transfer operators. SIAM Journal on Applied Dynamical Systems, 14 (3). pp. 1478-1517. ISSN 1536-0040

Blatt, M. and Burchardt, A. and Dedner, A. and Engwer, C. and Fahlke, J. and Flemisch, B. and Gersbacher, C. and Gräser, C. and Gruber, F. and Grüninger, C. and Kempf, D. and Klöfkorn, R. and Malkmus, T. and Müthing, S. and Nolte, M. and Piatkowski, M. and Sander, O. (2016) The Distributed and Unified Numerics Environment, Version 2.4. Archive of Numerical Software, 4 (100). pp. 13-29. ISSN 2197-8263

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

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

Caselles, V. and Igual, L. and Sander, O. (2006) An axiomatic approach to scalar data interpolation on surfaces. Numerische Mathematik, 102 (3). pp. 383-411. ISSN 0029-599X

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

Djurdjevac, N. and Bruckner, S. and Conrad, T. O. F. and Schütte, Ch. (2012) Random Walks on Complex Modular Networks. Journal of Numerical Analysis, Industrial and Applied Mathematics, 6 (1-2). pp. 29-50. ISSN 1790–8140

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

Duwal, S. and von Kleist, M. (2016) Top-down and bottom-up modelling in system pharmacology to understand clinical efficacy : An example with NRTIs of HIV-1. European Journal of Pharmaceutical Sciences, 94 . pp. 72-83. ISSN 0928-0987

Engwer, C. and Gräser, C. and Müthing, S. and Sander, O. (2018) Function space bases in the dune-functions module. arXiv:1806.09545 . pp. 1-53. (Submitted)

Engwer, C. and Gräser, C. and Müthing, S. and Sander, O. (2017) The interface for functions in the dune-functions module. Archive of Numerical Software, 5 (1). pp. 95-110. ISSN 2197-8263

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

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

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

Grohs, P. and Hardering, H. and Sander, O. (2015) Optimal a priori discretization error bounds for geodesic finite elements. Foundations of Computational Mathematics, 15 (6). pp. 1357-1411. ISSN 1615-3375

Gräser, C. (2013) Nonsmooth Schur-Newton methods for nonsmooth saddle point problems. Preprint 1004, Matheon Berlin .

Gräser, C. (2015) A note on Poincaré- and Friedrichs-type inequalities. arXiv:1512.02842 . (Submitted)

Gräser, C. and Alathur Srinivasan, P. A. (2020) Error bounds for PDE-regularized learning. arXiv:2003.06524 . pp. 1-20. (Submitted)

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

Gräser, C. and Kienle, D. and Sander, O. (2021) Truncated Nonsmooth Newton Multigrid for phase-field brittle-fracture problems. arXiv:2007.12290 . pp. 1-41. (Submitted)

Gräser, C. and Kies, T. (2019) Discretization error estimates for penalty formulations of a linearized Canham-Helfrich-type energy. IMA Journal of Numerical Analysis, 39 (2). pp. 626-649. ISSN 0272-4979

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

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

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

Gräser, C. and Sander, O. (2014) Polyhedral Gauß-Seidel converges. Journal of Numerical Mathematics, 22 (3). pp. 221-254. ISSN 1570-2820

Gräser, C. and Sander, O. (2014) Truncated nonsmooth Newton multigrid methods for simplex-constrained minimization problems. Preprint 384, IGPM Aachen . (Submitted)

Gräser, C. and Sander, O. (2009) The dune-subgrid module and some applications. Computing, 86 (4). pp. 269-290. ISSN 0010-485X

Gräser, Carsten and Sander, Oliver (2019) Truncated Nonsmooth Newton Multigrid Methods for Block-Separable Minimization Problems. IMA Journal of Numerical Analysis, 39 (1). pp. 454-481. ISSN 0272-4979

Hardering, H. (2013) Numerical approximation of capillary surfaces in a negative gravitational field. Interfaces and Free Boundaries, 15 (3). pp. 263-280. ISSN 1463-9971

Hartmann, C. and Schütte, Ch. (2012) Efficient rare event simulation by optimal nonequilibrium forcing. J. Stat. Mech. Theor. Exp., 2012 . P11004.

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

Heida, Martin and Schweizer, Ben (2018) Stochastic homogenization of plasticity equations. ESAIM: Control, Optimisation and Calculus of Variations, 24 (1). 153 -176.

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

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

Jouvet, G. and Bueler, E. (2012) Steady, shallow ice sheets as obstacle problems: Well-posedness and finite element approximation. SIAM J. Appl. Math., 72 (4). pp. 1292-1314. ISSN 0036-1399

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

Jouvet, G. and Funk, M. (2014) Modelling the trajectory of the corpses of mountaineers who disappeared in 1926 on Aletschgletscher, Switzerland. Journal of Glaciology, 60 (220). pp. 255-261. ISSN 0022-1430

Jouvet, G. and Gräser, C. (2013) An adaptive Newton multigrid method for a model of marine ice sheets. Journal of Computational Physics, 252 . pp. 419-437. ISSN 0021-9991

Jouvet, G. and Huss, M. and Funk, M. and Blatter, H. (2011) Modelling the retreat of Grosser Aletschgletscher, Switzerland, in a changing climate. Journal of Glaciology, 57 (206). pp. 1033-1045. ISSN 0022-1430

Jouvet, G. and Rappaz, J. (2011) Analysis and finite element approximation of a nonlinear stationary stokes problem arising in glaciology. Advances in Numerical Analysis, 2011 (Articl). ISSN 1687-9562

Kienle, D. and Gräser, C. and Sander, O. and Keip, M.-A. (2018) Efficient and reliable phase‐field simulation of brittle fracture using a nonsmooth multigrid solution scheme. PAMM. Special Issue: 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), 18 (1). e201800126. ISSN 1617-7061

Kies, T. and Gräser, C. (2021) On differentiability of the membrane-mediated mechanical interaction energy of discrete-continuum membrane-particle models. Interfaces and Free Boundaries . pp. 1-22. ISSN 1463-9963 (In Press)

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)

Kober, C. and Sader, R. and Thiele, H. and Bauer, H.-J. and Zeilhofer, H.-F. and Hoffmann, K.-H. (2000) FEM simulations versus biomechnical experiments concerning the human mandible: a comparision of the results of a frontal and a molar biting study. Preprint A-21-2000 . (Unpublished)

Kober, C. and Müller-Hannemann, M. (2001) A case study in hexahedral mesh generation: Simulation of the human mandible. Engineering with Computers, 17 (3). pp. 249-260. ISSN 0177-0667

Koltai, Péter and Volf, Alexander (2014) Optimizing the stable behavior of parameter-dependent dynamical systems --- maximal domains of attraction, minimal absorption times. Journal of Computational Dynamics, 1 (2). pp. 339-356. ISSN 2158-2491

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. 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

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

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

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

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

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

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. 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

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

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

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 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

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 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

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

Kornhuber, Ralf Fredholm integral equations for function approximation and the training of neural networks. (Submitted)

Krause, R. and Sander, O. (2006) Automatic construction of boundary parametrizations for geometric multigrid solvers. Computing and Visualization in Science, 9 (1). pp. 11-22. ISSN 1432-9360

Krause, R. and Wohlmuth, B. (2002) A Dirichlet-Neumann type algorithm for contact problems with friction. Computing and Visualization in Science, 5 (3). pp. 139-148. ISSN 1432-9360

Krause, R. and Wohlmuth, B. (2001) Domain decomposition methods on nonmatching grids and some applications to linear elasticity problems. Zeitschrift für angewandte Mathematik und Mechanik (ZAMM), 81 (Suppl.). pp. 21-24. ISSN 0044-2267

Krause, R. and Wohlmuth, B. (2000) Nonconforming decomposition methods: Techniques for linear elasticity. East-West Journal of Numerical Mathematics, 8 (3). pp. 177-206. ISSN 1569-3953; 0928-0200

Latorre, J.C. and Metzner, Ph. and Hartmann, C. and Schütte, Ch. (2011) A Structure-preserving numerical discretization of reversible diffusions. Commun. Math. Sci., 9 (4). pp. 1051-1072.

Leyendecker, S. and Hartmann, C. and Koch, M. (2012) Variational collision integrator for polymer chains. J. Comput. Phys, 231 (10). pp. 3896-3911.

Leyendecker, S. and Hartmann, C. and Koch, M. and Johnson, G. and Ortiz, M. (2012) Variational collision integrators in forward dynamics and optimal control. Proceedings of the 7th International Conference Croatian Society of Mechanics (7ICCSM2012) .

Lie, Han Cheng and Schütte, Ch. and Hartmann, C. (2014) Martingale-based gradient descent algorithm for estimating free energy values of diffusions. SIAM J. Sci. Comput. . ISSN 1064-8275 (Submitted)

Mielke, A. and Mittnenzweig, M. (2018) Convergence to Equilibrium in Energy-Reaction–Diffusion Systems Using Vector-Valued Functional Inequalities. Journal of Nonlinear Science . pp. 1-42. ISSN 1432-1467 (online)

Mielke, A. and Rossi, R. and Savaré, G. (2016) Balanced-Viscosity solutions for multi-rate systems. Journal of Physics: Conference Series, 727 . pp. 1-27.

Mireles, Victor and Conrad, T. O. F. (2015) Minimum-overlap clusterings and the sparsity of overcomplete decompositions of binary matrices. Procedia Computer Science, 51 . pp. 2967-2971. ISSN 1877-0509

Pattyn, F. and Perichon, L. and Durand, G. and Favier, L. and Gagliardini, O. and Hindmarsh, R. and Zwinger, T. and Albrecht, T. and Cornford, S. and Docquier, D. and Fuerst, J. and Goldberg, G. and Gudmundsson, G. H. and Humbert, A. and Huetten, M. and Huybrechts, P. and Jouvet, G. and Kleiner, T. and Larour, E. and Martin, D. (2013) Grounding-line migration in plan-view marine ice-sheet models: Results of the ice2sea MISMIP3d intercomparison. Journal of Glaciology, 59 (215). pp. 410-422. ISSN 0022-1430

Pipping, E. (2019) Existence of long-time solutions to dynamic problems of viscoelasticity with rate-and-state friction. ZAMM - Journal of Applied Mathematics and Mechanics . ISSN 1521-4001 (online)

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

Polthier, L. (2017) Algebraic Multilevel Methods for Markov Chains. SFB 1114 Preprint in arXiv:1711.04332 . pp. 1-19. (Unpublished)

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

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

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

Sander, O. (2010) Geodesic finite elements for Cosserat rods. International Journal for Numerical Methods in Engineering, 82 (13). pp. 1645-1670. ISSN 1097-0207

Sander, O. (2012) Geodesic finite elements on simplicial grids. International Journal for Numerical Methods in Engeneering, 92 (12). pp. 999-1025. ISSN Online: 1097-0207

Sander, O. (2011) The PSurface library. Computing and Visualization in Science, 14 (8). pp. 353-370. ISSN 1432-9360

Sander, O. (2006) A fast solver for finite deformation contact problems. Preprint A-06-02 . (Unpublished)

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

Sander, O. and Schiela, A. (2012) Energy minimizers of the coupling of a Cosserat rod to an elastic continuum. Mathematical Modelling, 7 (1). pp. 1118-1123.

Sander, O. and Schiela, A. (2014) Variational analysis of the coupling between a geometrically exact Cosserat rod and an elastic continuum. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 65 (6). pp. 1261-1288. ISSN 0044-2275 (Print) 1420-9039 (Online)

Sarich, M. and Banisch, Ralf and Hartmann, C. and Schütte, Ch. (2013) Markov State Models for Rare Events in Molecular Dynamics. Entropy (Special Issue), 16 (1). pp. 258-286. ISSN 1099-4300

Sarich, M. and Noé, F. and Schütte, Ch. (2010) On the Approximation Quality of Markov State Models. Multiscale Model. Simul., 8 (4). pp. 1154-1177.

Stange, H. and Brunken, S. and Greiner, D. and Heinemann, M. D. and Barragan Yani, D. A. and Wägele, L. A. and Li, Ch. and Simsek Sanli, E. and Kahnt, M. and Schmidt, S. S. and Bäcker, J.-P. and Kaufmann, Ch. A. and Klaus, M. and Scheer, R. and Genzel, Ch. and Mainz, R. (2019) Stacking fault reduction during annealing in Cu-poor CuInSe2 thin film solar cell absorbers analyzed by in situ XRD and grain growth modeling. Journal of Applied Physics, 125 (3). 035303. ISSN 0021-8979

Vater, S. and Klein, R. (2009) Stability of a Cartesian grid projection method for zero Froude number shallow water flows. Numerische Mathematik, 113 (1). pp. 123-161.

Vetter, A. and Liu, Y. and Witt, F. and Manjubala, I. and Sander, O. and Rao Epari, D. and Fratzl, P. and Duda, G. and Weinkamer, R. (2011) The mechanical heterogeneity of the hard callus influences local tissue strains during bone healing. Journal of Biomechanics, 44 (3). pp. 517-523. ISSN 0021-9290

Vetter, A. and Sander, O. and Duda, G. and Weinkamer, R. (2014) Healing of a mechano-responsive material. Europhysics Letters (EPL), 104 (6). pp. 1-6. ISSN 0295-5075

Vetter, A. and Witt, F. and Sander, O. and Duda, G. and Weinkamer, E. (2012) The spatio-temporal arrangement of different tissues during bone healing as a result of simple mechanobiological rules. Biomechanics and Modeling in Mechanobiology, 11 (1-2). pp. 147-160. ISSN 1617-7959

Wohlmuth, B. and Krause, R. (2001) A multigrid method based on the unconstrained product space for Mortar finite element discretizations. SIAM Journal on Numerical Analysis, 39 (1). pp. 192-213. ISSN 0036-1429

Wohlmuth, B. and Krause, R. (2003) Monotone methods on non-matching grids for non-linear contact problems. SIAM J. Sci. Comput., 25 (1). pp. 324-347. ISSN 1064-8275

Youett, J. and Sander, O. (2012) A dissipative discretization for large deformation frictionless dynamic contact problems. MATHEON Preprint #1184 .

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

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

Book Section

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

Bastian, P. and Buse, G. and Sander, O. (2010) Infrastructure for the Coupling of Dune Grids. In: Numerical Mathematics and Advanced Applications 2009: Proceedings of ENUMATH 2009. Springer Berlin Heidelberg, pp. 107-114. ISBN 978-3-642-11794-7

Berninger, H. (2009) Non-overlapping domain decomposition for the Richards equation via superposition operators. In: Domain Decomposition Methods in Science and Engineering XVIII. Lecture Notes in Computational Science and Engineering, 70 . Springer Berlin Heidelberg, pp. 169-176. ISBN 978-3-642-02676-8

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

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

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

Erdmann, B. and Kober, C. and Lang, J. and Deuflhard, P. and Zeilhofer, H.-F. and Sader, R. (2001) Efficient and reliable finite element methods for simulation of the human mandible. In: Proceedings of Medicine Meets Mathematics. Kloster Banz/Staffelstein. Report ZIB 01-14, 2001. (Submitted)

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

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

Gräser, C. (2008) Globalization of nonsmooth Newton methods for optimal control problems. In: Numerical Mathematics and Advanced Applications. Proceedings of ENUMATH 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications, Graz, Austria, September 2007 . Springer Berlin Heidelberg, pp. 605-612. ISBN 978-3-540-69776-3

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

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

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

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.

Jouvet, G. and Rappaz, J. (2014) Numerical analysis and simulation of the dynamics of mountain glaciers. In: Modeling, Simulation and Optimization for Science and Technology. Computational Methods in Applied Sciences (34). Springer Netherlands, pp. 83-92. ISBN 978-94-017-9053-6

Kober, C. (2000) Composite material with shape memory alloy fibers. In: Communications of the Bexbach Colloquium on Science 2000. Shaker, Aachen. ISBN 978-3-8322-1517-0

Kober, C. and Sader, R. and Zeilhofer, H.-F. and Prohaska, S. and Zachow, S. and Deuflhard, P. (2001) Anisotrope Materialmodellierung für den menschlichen Unterkiefer. In: Tagungsband des Workshops "Die Methode der Finiten Elemente in der Biomedizin, Biomechanik und angrenzenden Gebieten". Universitätsklinikum/Universitätsrechenzentrum, Ulm. ISBN 978-3980618342

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

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. 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. (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

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

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. 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

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

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

Krause, R. and Sander, O. (2005) Fast solving of contact problems on complicated geometries. In: Domain Decomposition Methods in Science and Engineering XIII. Lecture Notes in Computational Science and Engineering, 40 . Springer, Berlin, pp. 495-502. ISBN 978-3-540-22523-2

Krause, R. and Wohlmuth, B. (2000) Multigrid methods for Mortar finite elements. In: Multigrid Methods VI. Proceedings of the Sixth European Multigrid Conference Held in Gent, Belgium, September 27–30. Springer Berlin Heidelberg, pp. 136-142. ISBN 978-3-540-67157-2

Müller-Hannemann, M. and Kober, C. and Sader, R. and Zeilhofer, H.-F. (2001) Anisotropic validation of hexahedral meshes for composite materials in biomechanics. In: Proceedings of the 10th International Meshing Roundtable. International Meshing Roundtable, Newport Beach, CA, pp. 249-260.

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.

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

Sander, O. and Caselles, V. and Bertalmio, M. (2003) Axiomatic scalar data interpolation on manifolds. In: International Conference on Image Processing (ICIP) 2003. Proceedings. IEEE, Barcelona, Spain, pp. 681-684. ISBN 0-7803-7750-8

Sander, O. (2013) Coupling geometrically exact cosserat rods and linear elastic continua. In: Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, 91 . Springer Berlin Heidelberg, pp. 443-450. ISBN 978-3-642-35274-4

Sander, O. (2013) Geodesic finite elements in spaces of zero curvature. In: Numerical Mathematics and Advanced Applications 2011. Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011 . Springer Berlin Heidelberg, pp. 449-457. ISBN 978-3-642-33133-6

Ting, L. and Klein, R. (1991) Viscous Vortical Flows. In: Lecture Notes in Physics. Springer Verlag. ISBN 0387537139

Monograph

Vater, S. (2005) A New Projection Method for the Zero Froude Number Shallow Water Equations. Technical Report. Potsdam Institute for Climate Impact Research.

Vater, S. and Klein, R. (2007) Stability of a Cartesian grid projection method for zero Froude number shallow water flows. Technical Report. Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB).

Conference or Workshop Item

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

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

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

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

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.

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.

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

Thesis

Bernhard, S. (2006) Transient integral boundary layer method to simulate entrance flow conditions in one-dimensional arterial blood flow. PhD thesis, Georg-August-Universität Göttingen.