Edit Profile (opens in new tab) Schwab, Christoph Co-Author Distance Author ID: schwab.christoph Published as: Schwab, Christoph; Schwab, Ch.; Schwab, C.; Schwab, CH. more...less Homepage: https://www.math.ethz.ch/sam/the-institute/people/christoph-schwab.html External Links: MGP · Wikidata · dblp · GND Documents Indexed: 311 Publications since 1985, including 4 Books 7 Contributions as Editor Co-Authors: 180 Co-Authors with 302 Joint Publications 4,224 Co-Co-Authors all top 5 Co-Authors 14 single-authored 24 Schötzau, Dominik 15 Matache, Ana-Maria 13 Melenk, Jens Markus 12 Herrmann, Lukas 12 Mishra, Siddhartha 12 Zech, Jakob 10 Gerdes, Klaus 10 Kuo, Frances Y. 10 Wendland, Wolfgang L. 9 Dick, Josef 9 von Petersdorff, Tobias 8 Wihler, Thomas Pascal 7 Chernov, Alexey 7 Cohen, Albert 7 Feistauer, Miloslav 7 Hoang, Viet Ha 7 Le Gia, Quoc Thong 7 Marcati, Carlo 7 Schneider, Reinhold 7 Sloan, Ian Hugh 7 Süli, Endre E. 6 Gantner, Robert Nicholas 6 Hiptmair, Ralf 6 Lage, Christian 6 Reichmann, Oleg 6 Sauter, Stefan 6 Stevenson, Rob P. 6 Šukys, Jonas 6 Suri, Manil 6 Todor, Radu Alexandru 5 Babuška, Ivo 5 Gittelson, Claude Jeffrey 5 Jerez-Hanckes, Carlos 5 Kazeev, Vladimir A. 5 Opschoor, Joost A. A. 5 Schillings, Claudia 5 Toselli, Andrea 4 Andreev, Roman 4 Barth, Andrea 4 Dahmen, Wolfgang A. 4 Harbrecht, Helmut 4 Houston, Paul 4 Lang, Annika 4 Müller, Fabian Lukas 4 Perugia, Ilaria 4 Risebro, Nils Henrik 4 Winter, Christoph 3 Aylwin, Rubén 3 Bieri, Marcel 3 Buffa, Annalisa 3 Chen, Peng 3 Chkifa, Abdellah 3 DeVore, Ronald A. 3 Dolejší, Vít 3 Hilber, Norbert 3 Rakhuba, Maxim V. 3 Reich, Nils 3 Schmidlin, Gregor 3 Schulz, Heiko 3 Tokareva, Svetlana A. 3 Weber, Franziska 3 Welper, Gerrit 2 Abdulle, Assyr 2 Banjai, Lehel 2 Beuchler, Sven 2 Braess, Dietrich 2 Cockburn, Bernardo 2 Costabel, Martin 2 Dauge, Monique 2 Demkowicz, Leszek F. 2 Dinh Dũng 2 Eigel, Martin 2 Faustmann, Markus 2 Feischl, Michael 2 Frauenfelder, Philipp 2 Gonon, Lukas 2 Grella, Konstantin 2 Hackbusch, Wolfgang 2 Hansen, Markus 2 Henríquez, Fernando 2 Huang, Chunyan 2 Humphrey, Jay D. 2 Kozlov, Vladimir A. 2 Kunoth, Angela 2 Kutyniok, Gitta 2 Lim, Wang-Q 2 Longo, Marcello 2 Maz’ya, Vladimir Gilelevich 2 Moiola, Andrea 2 Oseledets, Ivan Valer’evich 2 Pentenrieder, Bastian 2 Petersen, Philipp Christian 2 Quek, Jia Hao 2 Scheichl, Robert 2 Stenberg, Rolf 2 Sterz, Oliver 2 Stuart, Andrew M. 2 Xanthis, Leonidas Spyridon 2 Zander, Elmar K. 1 Actis, Ricardo L. ...and 88 more Co-Authors all top 5 Serials 25 SIAM Journal on Numerical Analysis 24 Numerische Mathematik 18 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 12 Computer Methods in Applied Mechanics and Engineering 12 Mathematics of Computation 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 IMA Journal of Numerical Analysis 8 Journal of Computational Physics 8 SIAM Journal on Scientific Computing 8 SIAM/ASA Journal on Uncertainty Quantification 6 Inverse Problems 6 SIAM Journal on Mathematical Analysis 6 Foundations of Computational Mathematics 6 Analysis and Applications (Singapore) 4 Computers & Mathematics with Applications 4 BIT 4 Calcolo 4 Computing 4 Journal of Computational and Applied Mathematics 4 Applied Numerical Mathematics 4 Advances in Computational Mathematics 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 4 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 4 Multiscale Modeling & Simulation 4 Lecture Notes in Computational Science and Engineering 3 Constructive Approximation 3 Journal of Scientific Computing 3 Finance and Stochastics 3 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 3 The ANZIAM Journal 3 Stochastic and Partial Differential Equations. Analysis and Computations 2 Mathematical Methods in the Applied Sciences 2 International Journal for Numerical Methods in Engineering 2 Mathematische Nachrichten 2 Numerical Methods for Partial Differential Equations 2 Journal of Elasticity 2 Comptes Rendus de l’Académie des Sciences. Série I 2 East-West Journal of Numerical Mathematics 2 Computing and Visualization in Science 2 Oberwolfach Reports 1 Archive for Rational Mechanics and Analysis 1 International Journal of Solids and Structures 1 Integral Equations and Operator Theory 1 Journal of Approximation Theory 1 Journal für die Reine und Angewandte Mathematik 1 Mathematics and Computers in Simulation 1 SIAM Journal on Control and Optimization 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Computational Mechanics 1 SIAM Journal on Matrix Analysis and Applications 1 Mathematica Bohemica 1 The Annals of Applied Probability 1 Applications of Mathematics 1 Numerical Algorithms 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Linear Algebra and its Applications 1 Mathematical Modelling and Scientific Computing 1 Engineering Analysis with Boundary Elements 1 Journal of Geodesy 1 Vietnam Journal of Mathematics 1 Journal of Mathematical Fluid Mechanics 1 Quantitative Finance 1 Computational Methods in Applied Mathematics 1 Journal of Hyperbolic Differential Equations 1 Acta Numerica 1 Springer Series in Computational Mathematics 1 Research in the Mathematical Sciences 1 Springer Finance 1 Numerical Mathematics and Scientific Computation all top 5 Fields 252 Numerical analysis (65-XX) 170 Partial differential equations (35-XX) 72 Probability theory and stochastic processes (60-XX) 42 Fluid mechanics (76-XX) 31 Mechanics of deformable solids (74-XX) 25 Approximations and expansions (41-XX) 17 Computer science (68-XX) 15 Integral equations (45-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Statistics (62-XX) 10 Optics, electromagnetic theory (78-XX) 9 Operator theory (47-XX) 7 General and overarching topics; collections (00-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Functions of a complex variable (30-XX) 6 Ordinary differential equations (34-XX) 5 Potential theory (31-XX) 5 Functional analysis (46-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Real functions (26-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Biology and other natural sciences (92-XX) 2 Number theory (11-XX) 2 Special functions (33-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Systems theory; control (93-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 292 Publications have been cited 7,416 times in 3,814 Documents Cited by ▼ Year ▼ \(p\)- and \(hp\)-finite element methods. Theory and applications in solid and fluid mechanics. Zbl 0910.73003Schwab, Ch. 362 1998 Boundary element methods. Zbl 1215.65183Sauter, Stefan A.; Schwab, Christoph 236 2011 Discontinuous \(hp\)-finite element methods for advection-diffusion-reaction problems. Zbl 1015.65067Houston, Paul; Schwab, Christoph; Süli, Endre 231 2002 Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDE’s. Zbl 1219.35379Cohen, Albert; DeVore, Ronald; Schwab, Christoph 158 2011 Karhunen-Loève approximation of random fields by generalized fast multipole methods. Zbl 1104.65008Schwab, Christoph; Todor, Radu Alexandru 155 2006 Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs. Zbl 1206.60064Cohen, Albert; DeVore, Ronald; Schwab, Christoph 152 2010 Finite elements for elliptic problems with stochastic coefficients. Zbl 1143.65392Frauenfelder, Philipp; Schwab, Christoph; Todor, Radu Alexandru 150 2005 Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients. Zbl 1230.65006Barth, Andrea; Schwab, Christoph; Zollinger, Nathaniel 149 2011 Local discontinuous Galerkin methods for the Stokes system. Zbl 1032.65127Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik; Schwab, Christoph 135 2002 Optimal a priori error estimates for the \(hp\)-version of the local discontinuous Galerkin method for convection-diffusion problems. Zbl 0997.65111Castillo, Paul; Cockburn, Bernardo; Schötzau, Dominik; Schwab, Christoph 135 2002 Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs. Zbl 1269.65010Schwab, Christoph; Gittelson, Claude Jeffrey 122 2011 Quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients. Zbl 1271.65017Kuo, Frances Y.; Schwab, Christoph; Sloan, Ian H. 107 2012 Time discretization of parabolic problems by the \(hp\)-version of the discontinuous Galerkin finite element method. Zbl 0978.65091Schötzau, Dominik; Schwab, Christoph 105 2000 Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients. Zbl 1120.65004Todor, Radu Alexandru; Schwab, Christoph 99 2007 Space-time adaptive wavelet methods for parabolic evolution problems. Zbl 1198.65249Schwab, Christoph; Stevenson, Rob 91 2009 The \(p\) and \(hp\) versions of the finite element method for problems with boundary layers. Zbl 0853.65115Schwab, Christoph; Suri, Manil 83 1996 Mixed hp-DGFEM for incompressible flows. Zbl 1055.76032Schötzau, Dominik; Schwab, Christoph; Toselli, Andrea 79 2003 High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs. Zbl 1298.65022Chkifa, Abdellah; Cohen, Albert; Schwab, Christoph 78 2014 Tensor-structured Galerkin approximation of parametric and stochastic elliptic PDEs. Zbl 1243.65009Khoromskij, Boris N.; Schwab, Christoph 77 2011 Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs. Zbl 1327.65251Chkifa, Abdellah; Cohen, Albert; Schwab, Christoph 71 2015 An \(hp\) a priori error analysis of the DG time-stepping for initial value problems. Zbl 1012.65084Schötzau, Dominik; Schwab, Christoph 68 2000 Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients. Zbl 1341.65003Graham, I. G.; Kuo, F. Y.; Nichols, J. A.; Scheichl, R.; Schwab, Ch.; Sloan, I. H. 68 2015 Isotropic Gaussian random fields on the sphere: regularity, fast simulation and stochastic partial differential equations. Zbl 1328.60126Lang, Annika; Schwab, Christoph 65 2015 Adaptive stochastic Galerkin FEM. Zbl 1296.65157Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar 65 2014 Sparse finite elements for elliptic problems with stochastic loading. Zbl 1044.65085Schwab, Christoph; Todor, Radu-Alexandru 65 2003 Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data. Zbl 1271.65018Mishra, Siddhartha; Schwab, Christoph 64 2012 Sparse high order FEM for elliptic sPDEs. Zbl 1157.65481Bieri, Marcel; Schwab, Christoph 59 2009 Sparse, adaptive Smolyak quadratures for Bayesian inverse problems. Zbl 1278.65008Schillings, Claudia; Schwab, Christoph 59 2013 Adaptive Petrov-Galerkin methods for first order transport equations. Zbl 1260.65091Dahmen, Wolfgang; Huang, Chunyan; Schwab, Christoph; Welper, Gerrit 57 2012 Stabilized \(hp\)-finite element methods for first-order hyperbolic problems. Zbl 0957.65103Houston, Paul; Schwab, Christoph; Süli, Endre 57 2000 On numerical cubatures of singular surface integrals in boundary element methods. Zbl 0761.65012Schwab, Christoph; Wendland, Wolfgang L. 56 1992 Boundary element methods for Maxwell transmission problems in Lipschitz domains. Zbl 1071.65160Buffa, Annalisa; Hiptmair, Ralf; von Petersdorff, Tobias; Schwab, Christoph 56 2003 Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions. Zbl 1402.76083Mishra, S.; Schwab, Ch.; Šukys, J. 56 2012 Numerical solution of parabolic equations in high dimensions. Zbl 1083.65095von Petersdorff, Tobias; Schwab, Christoph 53 2004 Sparse second moment analysis for elliptic problems in stochastic domains. Zbl 1146.65007Harbrecht, Helmut; Schneider, Reinhold; Schwab, Christoph 53 2008 Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs. Zbl 1326.65013Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Nuyens, Dirk; Schwab, Christoph 53 2014 Wavelet approximations for first kind boundary integral equations on polygons. Zbl 0863.65074von Petersdorff, Tobias; Schwab, Christoph 52 1996 Fast deterministic pricing of options on Lévy driven assets. Zbl 1072.60052Matache, Ana-Maria; von Petersdorff, Tobias; Schwab, Christoph 51 2004 Sparse deterministic approximation of Bayesian inverse problems. Zbl 1236.62014Schwab, C.; Stuart, A. M. 49 2012 An adaptive wavelet method for solving high-dimensional elliptic PDEs. Zbl 1205.65313Dijkema, Tammo Jan; Schwab, Christoph; Stevenson, Rob 48 2009 Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients. Zbl 1318.65006Kuo, Frances Y.; Schwab, Christoph; Sloan, Ian H. 48 2015 High-dimensional finite elements for elliptic problems with multiple scales. Zbl 1074.65135Viet Ha Hoang; Schwab, Christoph 47 2005 Boundary element methods for Maxwell’s equations on non-smooth domains. Zbl 1019.65094Buffa, Annalisa; Costabel, Martin; Schwab, Christoph 47 2002 Deep learning in high dimension: neural network expression rates for generalized polynomial chaos expansions in UQ. Zbl 1478.68309Schwab, Christoph; Zech, Jakob 46 2019 Fully discrete \(hp\)-finite elements: Fast quadrature. Zbl 0985.65141Melenk, J. M.; Gerdes, K.; Schwab, Ch. 45 2001 Wavelet Galerkin pricing of American options on Lévy driven assets. Zbl 1134.91450Matache, Ana-Maria; Nitsche, Pál-Andrej; Schwab, Christoph 45 2005 Existence of global weak solutions for some polymeric flow models. Zbl 1161.76453Barrett, John W.; Schwab, Christoph; Süli, Endre 44 2005 Complexity analysis of accelerated MCMC methods for Bayesian inversion. Zbl 1288.65004Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M. 44 2013 Sparse finite elements for stochastic elliptic problems — higher order moments. Zbl 1044.65006Schwab, Ch.; Todor, R. A. 42 2003 Sparse tensor discretization of elliptic SPDEs. Zbl 1205.35346Bieri, Marcel; Andreev, Roman; Schwab, Christoph 40 2009 Quasi-Monte Carlo methods for high-dimensional integration: the standard (weighted Hilbert space) setting and beyond. Zbl 1248.65001Kuo, F. Y.; Schwab, Ch.; Sloan, I. H. 40 2011 Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs. Zbl 1273.65009Chkifa, Abdellah; Cohen, Albert; Devore, Ronald; Schwab, Christoph 40 2013 Wavelet Galerkin algorithms for boundary integral equations. Zbl 0943.65134Lage, Christian; Schwab, Christoph 40 1999 Kernel properties and representations of boundary integral operators. Zbl 0805.35168Schwab, Christoph; Wendland, Wolfgang L. 38 1992 Fast numerical solution of parabolic integro-differential equations with applications in finance. Zbl 1098.65123Matache, Ana-Maria; Schwab, Christoph; Wihler, Thomas P. 38 2005 The \(hp\) finite element method for problems in mechanics with boundary layers. Zbl 0959.74073Schwab, Christoph; Suri, Manil; Xenophontos, C. 38 1998 Exponential convergence of \(hp\)-FEM for Maxwell equations with weighted regularization in polygonal domains. Zbl 1078.65089Costabel, Martin; Dauge, Monique; Schwab, Christoph 37 2005 \(hp\)-discontinuous Galerkin time stepping for parabolic problems. Zbl 0992.65103Werder, T.; Gerdes, K.; Schötzau, Dominik; Schwab, Christoph 37 2001 A posteriori modeling error estimation for hierarchic plate models. Zbl 0856.73031Schwab, Christoph 37 1996 Sparse finite element methods for operator equations with stochastic data. Zbl 1164.65300von Petersdorff, Tobias; Schwab, Christoph 34 2006 Deep ReLU networks and high-order finite element methods. Zbl 1452.65354Opschoor, Joost A. A.; Petersen, Philipp C.; Schwab, Christoph 34 2020 Multilevel quasi-Monte Carlo methods for lognormal diffusion problems. Zbl 1368.65005Kuo, Frances Y.; Scheichl, Robert; Schwab, Christoph; Sloan, Ian H.; Ullmann, Elisabeth 33 2017 Variable order composite quadrature of singular and nearly singular integrals. Zbl 0813.65057Schwab, Christoph 32 1994 Heterogeneous multiscale FEM for diffusion problems on rough surfaces. Zbl 1160.65337Abdulle, Assyr; Schwab, Christoph 31 2005 Multiwavelets for second-kind integral equations. Zbl 0891.65121Von Petersdorff, Tobias; Schwab, Christoph; Schneider, Reinhold 31 1997 Multilevel higher-order quasi-Monte Carlo Bayesian estimation. Zbl 1375.65169Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph 31 2017 \(hp\) FEM for reaction-diffusion equations. I: Robust exponential convergence. Zbl 0972.65093Melenk, Jens Markus; Schwab, Christoph 30 1998 Locking effects in the finite element approximation of plate models. Zbl 0827.73063Suri, Manil; Babuška, Ivo; Schwab, Christoph 30 1995 Computational methods for quantitative finance. Finite element methods for derivative pricing. Zbl 1275.91005Hilber, Norbert; Reichmann, Oleg; Schwab, Christoph; Winter, Christoph 30 2013 Multilevel Monte Carlo method for parabolic stochastic partial differential equations. Zbl 1272.65009Barth, Andrea; Lang, Annika; Schwab, Christoph 30 2013 A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes. Zbl 1335.65006Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar 30 2015 Analytic regularity and GPC approximation for control problems constrained by linear parametric elliptic and parabolic PDEs. Zbl 1278.49043Kunoth, Angela; Schwab, Christoph 28 2013 Natural boundary element methods for the electric field integral equation on polyhedra. Zbl 1010.78014Hiptmair, Ralf; Schwab, Christoph 27 2002 Quadrature for \(hp\)-Galerkin BEM in \(\mathbb{R}^3\). Zbl 0901.65069Sauter, Stefan A.; Schwab, Christoph 27 1997 Multilevel frames for sparse tensor product spaces. Zbl 1151.65010Harbrecht, Helmut; Schneider, Reinhold; Schwab, Christoph 27 2008 A finite volume discontinuous Galerkin scheme for nonlinear convection-diffusion problems. Zbl 1098.65095Dolejší, Vít; Feistauer, Miloslav; Schwab, Christoph 27 2002 \(hp\)-dGFEM for second order elliptic problems in polyhedra. II: Exponential convergence. Zbl 1457.65215Schötzau, D.; Schwab, Ch.; Wihler, T. P. 27 2013 Hierarchic models for laminated plates and shells. Zbl 0959.74061Actis, Ricardo L.; Szabo, Barna A.; Schwab, Christoph 27 1999 Multilevel higher order QMC Petrov-Galerkin discretization for affine parametric operator equations. Zbl 1347.65012Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph 27 2016 Large deformation shape uncertainty quantification in acoustic scattering. Zbl 1402.35321Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch. 27 2018 Fourier mode analysis of layers in shallow shell deformations. Zbl 0983.74039Pitkäranta, Juhani; Matache, Ana-Maria; Schwab, Christoph 26 2001 Exponential convergence of {\(hp\)} quadrature for integral operators with Gevrey kernels. Zbl 1269.65143Chernov, Alexey; Von Petersdorff, Tobias; Schwab, Christoph 26 2011 Analytic regularity of Stokes flow on polygonal domains in countably weighted Sobolev spaces. Zbl 1121.35098Guo, Benqi; Schwab, Christoph 26 2006 Sparsity in Bayesian inversion of parametric operator equations. Zbl 1291.65033Schillings, Claudia; Schwab, Christoph 26 2014 \(N\)-term Wiener chaos approximation rates for elliptic PDEs with lognormal Gaussian random inputs. Zbl 1294.65010Hoang, Viet Ha; Schwab, Christoph 26 2014 Two-scale FEM for homogenization problems. Zbl 1070.65572Matache, Ana-Maria; Schwab, Christoph 26 2002 Higher order quasi-Monte Carlo integration for holomorphic, parametric operator equations. Zbl 1398.65031Dick, Josef; Le Gia, Quoc T.; Schwab, Christoph 25 2016 Sparse-grid, reduced-basis Bayesian inversion. Zbl 1425.65020Chen, Peng; Schwab, Christoph 25 2015 Tensor FEM for spectral fractional diffusion. Zbl 1429.65272Banjai, Lehel; Melenk, Jens M.; Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.; Schwab, Christoph 25 2019 Numerical methods for Lévy processes. Zbl 1195.91175Hilber, N.; Reich, N.; Schwab, C.; Winter, C. 24 2009 Boundary elements methods. Analysis, numerics and implementation of fast algorithms. (Randelementmethoden. Analyse, Numerik und Implementierung schneller Algorithmen.) Zbl 1059.65108Sauter, Stefan; Schwab, Christoph 24 2004 On some aspects of the discontinuous Galerkin finite element method for conservation laws. Zbl 1013.65108Dolejší, Vít; Feistauer, Miloslav; Schwab, Christoph 24 2003 Sparse-grid, reduced-basis Bayesian inversion: nonaffine-parametric nonlinear equations. Zbl 1349.62076Chen, Peng; Schwab, Christoph 24 2016 HP90: A general and flexible Fortran 90 \(hp\)-FE code. Zbl 0912.68014Demkowicz, L.; Gerdes, K.; Schwab, C.; Bajer, A.; Walsh, T. 23 1998 A posteriori error estimation for hierarchic models of elliptic boundary value problems on thin domains. Zbl 0846.65056Babuška, Ivo; Schwab, Christoph 23 1996 Sparse adaptive finite elements for radiative transfer. Zbl 1147.65095Widmer, G.; Hiptmair, R.; Schwab, Ch. 23 2008 \(hp\)-dGFEM for second-order elliptic problems in polyhedra I: Stability on geometric meshes. Zbl 1276.65084Schötzau, Dominik; Schwab, Christoph; Wihler, Thomas Pascal 23 2013 Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions. Zbl 1382.65409Kazeev, Vladimir; Schwab, Christoph 23 2018 Electromagnetic wave scattering by random surfaces: shape holomorphy. Zbl 1381.35170Jerez-Hanckes, Carlos; Schwab, Christoph; Zech, Jakob 23 2017 Sparse finite element approximation of high-dimensional transport-dominated diffusion problems. Zbl 1159.65094Schwab, Christoph; Süli, Endre; Todor, Radu Alexandru 22 2008 Exponential ReLU neural network approximation rates for point and edge singularities. Zbl 1519.35253Marcati, Carlo; Opschoor, Joost A. A.; Petersen, Philipp C.; Schwab, Christoph 1 2023 DNN expression rate analysis of high-dimensional PDEs: application to option pricing. Zbl 1500.35009Elbrächter, Dennis; Grohs, Philipp; Jentzen, Arnulf; Schwab, Christoph 22 2022 Exponential ReLU DNN expression of holomorphic maps in high dimension. Zbl 1500.41008Opschoor, J. A. A.; Schwab, Ch.; Zech, J. 14 2022 Weighted analytic regularity for the integral fractional Laplacian in polygons. Zbl 1505.35070Faustmann, Markus; Marcati, Carlo; Melenk, Jens Markus; Schwab, Christoph 3 2022 Tensor rank bounds for point singularities in \(\mathbb{R}^3\). Zbl 1487.35019Marcati, C.; Rakhuba, M.; Schwab, Ch. 2 2022 Deep solution operators for variational inequalities via proximal neural networks. Zbl 07546269Schwab, Christoph; Stein, Andreas 1 2022 Quantized tensor FEM for multiscale problems: diffusion problems in two and three dimensions. Zbl 1496.65220Kazeev, Vladimir; Oseledets, Ivan; Rakhuba, Maxim V.; Schwab, Christoph 1 2022 Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models. Zbl 1475.91356Gonon, Lukas; Schwab, Christoph 5 2021 Space-time discontinuous Galerkin approximation of acoustic waves with point singularities. Zbl 07528299Bansal, Pratyuksh; Moiola, Andrea; Perugia, Ilaria; Schwab, Christoph 5 2021 Shape holomorphy of the Calderón projector for the Laplacian in \(\mathbb{R}^2\). Zbl 1472.45011Henríquez, Fernando; Schwab, Christoph 3 2021 Higher-order quasi-Monte Carlo training of deep neural networks. Zbl 1492.65043Longo, Marcello; Mishra, Siddhartha; Rusch, T. Konstantin; Schwab, Christoph 2 2021 Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems. Zbl 1478.65107Herrmann, Lukas; Keller, Magdalena; Schwab, Christoph 1 2021 Multilevel Markov chain Monte Carlo for Bayesian inversion of parabolic partial differential equations under Gaussian prior. Zbl 1465.65006Hoang, Viet Ha; Quek, Jia Hao; Schwab, Christoph 1 2021 Exponential convergence of mixed \(hp\)-DGFEM for the incompressible Navier-Stokes equations in \(\mathbb{R}^2\). Zbl 1519.65057Schötzau, Dominik; Marcati, Carlo; Schwab, Christoph 1 2021 Deep ReLU networks and high-order finite element methods. Zbl 1452.65354Opschoor, Joost A. A.; Petersen, Philipp C.; Schwab, Christoph 34 2020 Convergence rates of high dimensional Smolyak quadrature. Zbl 07240638Zech, Jakob; Schwab, Christoph 14 2020 Domain uncertainty quantification in computational electromagnetics. Zbl 1483.65010Aylwin, Ruben; Jerez-Hanckes, Carlos; Schwab, Christoph; Zech, Jakob 8 2020 Deep neural network expression of posterior expectations in Bayesian PDE inversion. Zbl 1453.35191Herrmann, Lukas; Schwab, Christoph; Zech, Jakob 8 2020 Multilevel approximation of Gaussian random fields: fast simulation. Zbl 1448.60110Herrmann, Lukas; Kirchner, Kristin; Schwab, Christoph 7 2020 Exponential convergence in \(H^1\) of hp-FEM for Gevrey regularity with isotropic singularities. Zbl 1433.65290Feischl, M.; Schwab, Ch. 3 2020 Multilevel quasi-Monte Carlo uncertainty quantification for advection-diffusion-reaction. Zbl 07240088Herrmann, Lukas; Schwab, Christoph 3 2020 Analytic regularity for the incompressible Navier-Stokes equations in polygons. Zbl 1447.35252Marcati, Carlo; Schwab, Christoph 2 2020 Analysis of a multilevel Markov chain Monte Carlo finite element method for Bayesian inversion of log-normal diffusions. Zbl 1491.65010Hoang, Viet Ha; Quek, Jia Hao; Schwab, Christoph 2 2020 Deep learning in high dimension: neural network expression rates for generalized polynomial chaos expansions in UQ. Zbl 1478.68309Schwab, Christoph; Zech, Jakob 46 2019 Tensor FEM for spectral fractional diffusion. Zbl 1429.65272Banjai, Lehel; Melenk, Jens M.; Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.; Schwab, Christoph 25 2019 Multilevel approximation of parametric and stochastic PDES. Zbl 1427.65386Zech, Jakob; Dũng, Dinh; Schwab, Christoph 14 2019 Higher order quasi-Monte Carlo integration for Bayesian PDE inversion. Zbl 1442.62051Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph 11 2019 Multilevel quasi-Monte Carlo integration with product weights for elliptic PDEs with lognormal coefficients. Zbl 07135561Herrmann, Lukas; Schwab, Christoph 11 2019 QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights. Zbl 07006664Herrmann, Lukas; Schwab, Christoph 10 2019 Improved efficiency of a multi-index FEM for computational uncertainty quantification. Zbl 07100359Dick, Josef; Feischl, Michael; Schwab, Christoph 4 2019 Uncertainty quantification for spectral fractional diffusion: sparsity analysis of parametric solutions. Zbl 1469.65170Herrmann, Lukas; Schwab, Christoph; Zech, Jakob 2 2019 Large deformation shape uncertainty quantification in acoustic scattering. Zbl 1402.35321Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch. 27 2018 Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions. Zbl 1382.65409Kazeev, Vladimir; Schwab, Christoph 23 2018 Shape holomorphy of the stationary Navier-Stokes equations. Zbl 1390.35227Cohen, Albert; Schwab, Christoph; Zech, Jakob 18 2018 Quasi-Monte Carlo integration for affine-parametric, elliptic PDEs: local supports and product weights. Zbl 1378.65072Gantner, Robert N.; Herrmann, Lukas; Schwab, Christoph 15 2018 Numerical analysis of lognormal diffusions on the sphere. Zbl 1402.60062Herrmann, Lukas; Lang, Annika; Schwab, Christoph 10 2018 Multilevel QMC with product weights for affine-parametric, elliptic PDEs. Zbl 1405.65008Gantner, Robert N.; Herrmann, Lukas; Schwab, Christoph 10 2018 Space-time \(hp\)-approximation of parabolic equations. Zbl 1404.65118Devaud, Denis; Schwab, Christoph 7 2018 QMC algorithms with product weights for lognormal-parametric, elliptic PDEs. Zbl 1422.65017Herrmann, Lukas; Schwab, Christoph 6 2018 Adaptive anisotropic Petrov-Galerkin methods for first order transport equations. Zbl 1435.65197Dahmen, Wolfgang; Kutyniok, Gitta; Lim, Wang-Q; Schwab, Christoph; Welper, Gerrit 5 2018 Exponential convergence of \(hp\)-FEM for elliptic problems in polyhedra: mixed boundary conditions and anisotropic polynomial degrees. Zbl 1402.65166Schötzau, Dominik; Schwab, Christoph 4 2018 Discontinuous Galerkin methods for acoustic wave propagation in polygons. Zbl 1406.65080Müller, Fabian; Schötzau, Dominik; Schwab, Christoph 4 2018 Correction to: “Multilevel Monte Carlo front-tracking for random scalar conservation laws”. Zbl 1430.65004Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska 1 2018 Multilevel quasi-Monte Carlo methods for lognormal diffusion problems. Zbl 1368.65005Kuo, Frances Y.; Scheichl, Robert; Schwab, Christoph; Sloan, Ian H.; Ullmann, Elisabeth 33 2017 Multilevel higher-order quasi-Monte Carlo Bayesian estimation. Zbl 1375.65169Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph 31 2017 Electromagnetic wave scattering by random surfaces: shape holomorphy. Zbl 1381.35170Jerez-Hanckes, Carlos; Schwab, Christoph; Zech, Jakob 23 2017 Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations. Zbl 1358.65034Rauhut, Holger; Schwab, Christoph 20 2017 Fully discrete approximation of parametric and stochastic elliptic PDEs. Zbl 1377.65005Bachmayr, Markus; Cohen, Albert; Dũng, Dinh; Schwab, Christoph 18 2017 Covariance regularity and \(\mathcal {H}\)-matrix approximation for rough random fields. Zbl 1362.65124Dölz, J.; Harbrecht, H.; Schwab, Ch. 15 2017 Fractional space-time variational formulations of (Navier-) Stokes equations. Zbl 1375.35329Schwab, Christoph; Stevenson, Rob 12 2017 A multilevel Monte Carlo finite difference method for random scalar degenerate convection-diffusion equations. Zbl 1373.35179Koley, Ujjwal; Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska 11 2017 Electromagnetic wave scattering by random surfaces: uncertainty quantification via sparse tensor boundary elements. Zbl 1433.78013Jerez-Hanckes, Carlos; Schwab, Christoph 9 2017 QTT-finite-element approximation for multiscale problems. I: Model problems in one dimension. Zbl 1375.65152Kazeev, Vladimir; Oseledets, Ivan; Rakhuba, Maxim; Schwab, Christoph 8 2017 Symmetric interior penalty discontinuous Galerkin methods for elliptic problems in polygons. Zbl 1376.65145Müller, Fabian; Schötzau, Dominik; Schwab, Christoph 5 2017 Monte-Carlo finite-volume methods in uncertainty quantification for hyperbolic conservation laws. Zbl 1407.65150Mishra, Siddhartha; Schwab, Christoph 3 2017 Multilevel higher order QMC Petrov-Galerkin discretization for affine parametric operator equations. Zbl 1347.65012Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph 27 2016 Higher order quasi-Monte Carlo integration for holomorphic, parametric operator equations. Zbl 1398.65031Dick, Josef; Le Gia, Quoc T.; Schwab, Christoph 25 2016 Sparse-grid, reduced-basis Bayesian inversion: nonaffine-parametric nonlinear equations. Zbl 1349.62076Chen, Peng; Schwab, Christoph 24 2016 Computational higher order quasi-Monte Carlo integration. Zbl 1356.65003Gantner, Robert N.; Schwab, Christoph 22 2016 Numerical solution of scalar conservation laws with random flux functions. Zbl 1343.65007Mishra, Siddhartha; Risebro, Nils Henrik; Schwab, Christoph; Tokareva, Svetlana 22 2016 Scaling limits in computational Bayesian inversion. Zbl 1358.65013Schillings, Claudia; Schwab, Christoph 20 2016 Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium. Zbl 1351.76117Mishra, S.; Schwab, Ch.; Šukys, J. 16 2016 Sparse adaptive tensor Galerkin approximations of stochastic PDE-constrained control problems. Zbl 1398.65252Kunoth, Angela; Schwab, Christoph 13 2016 Adaptive sparse grid model order reduction for fast Bayesian estimation and inversion. Zbl 1337.65012Chen, Peng; Schwab, Christoph 12 2016 \(hp\)-dGFEM for second-order mixed elliptic problems in polyhedra. Zbl 1332.65173Schötzau, Dominik; Schwab, Christoph; Wihler, Thomas P. 10 2016 Finite elements with mesh refinement for elastic wave propagation in polygons. Zbl 1457.65130Müller, Fabian; Schwab, Christoph 7 2016 Multilevel Monte Carlo front-tracking for random scalar conservation laws. Zbl 1350.65008Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska 7 2016 Numerical approximation of statistical solutions of planar, incompressible flows. Zbl 1416.76184Leonardi, Filippo; Mishra, Siddhartha; Schwab, Christoph 3 2016 Multilevel Monte Carlo simulation of statistical solutions to the Navier-Stokes equations. Zbl 1382.76209Barth, Andrea; Schwab, Christoph; Šukys, Jonas 2 2016 Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs. Zbl 1327.65251Chkifa, Abdellah; Cohen, Albert; Schwab, Christoph 71 2015 Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients. Zbl 1341.65003Graham, I. G.; Kuo, F. Y.; Nichols, J. A.; Scheichl, R.; Schwab, Ch.; Sloan, I. H. 68 2015 Isotropic Gaussian random fields on the sphere: regularity, fast simulation and stochastic partial differential equations. Zbl 1328.60126Lang, Annika; Schwab, Christoph 65 2015 Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients. Zbl 1318.65006Kuo, Frances Y.; Schwab, Christoph; Sloan, Ian H. 48 2015 A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes. Zbl 1335.65006Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar 30 2015 Sparse-grid, reduced-basis Bayesian inversion. Zbl 1425.65020Chen, Peng; Schwab, Christoph 25 2015 Finite elements with mesh refinement for wave equations in polygons. Zbl 1311.65126Müller, Fabian L.; Schwab, Christoph 14 2015 Tensor approximation of stationary distributions of chemical reaction networks. Zbl 1322.60155Kazeev, Vladimir; Schwab, Christoph 10 2015 Exponential convergence for \(hp\)-version and spectral finite element methods for elliptic problems in polyhedra. Zbl 1322.65099Schötzau, Dominik; Schwab, Christoph 8 2015 Fast QMC matrix-vector multiplication. Zbl 1320.65008Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph 5 2015 Quadrature algorithms for high dimensional singular integrands on simplices. Zbl 1332.65035Chernov, Alexey; von Petersdorff, Tobias; Schwab, Christoph 4 2015 Exponential convergence of simplicial hp-FEM for \(H^1\)-functions with isotropic singularities. Zbl 1352.65548Schwab, Christoph 1 2015 Higher order quasi Monte-Carlo integration in uncertainty quantification. Zbl 1352.65017Dick, Josef; Thong Le Gia, Quoc; Schwab, Christoph 1 2015 High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs. Zbl 1298.65022Chkifa, Abdellah; Cohen, Albert; Schwab, Christoph 78 2014 Adaptive stochastic Galerkin FEM. Zbl 1296.65157Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar 65 2014 Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs. Zbl 1326.65013Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Nuyens, Dirk; Schwab, Christoph 53 2014 Sparsity in Bayesian inversion of parametric operator equations. Zbl 1291.65033Schillings, Claudia; Schwab, Christoph 26 2014 \(N\)-term Wiener chaos approximation rates for elliptic PDEs with lognormal Gaussian random inputs. Zbl 1294.65010Hoang, Viet Ha; Schwab, Christoph 26 2014 Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz \(hp\)-dGFEM. Zbl 1295.31004Hiptmair, Ralf; Moiola, Andrea; Perugia, Ilaria; Schwab, Christoph 15 2014 Exponential convergence of the \(hp\) version of isogeometric analysis in 1D. Zbl 1282.65090Buffa, Annalisa; Sangalli, Giancarlo; Schwab, Christoph 8 2014 Space-time variational saddle point formulations of Stokes and Navier-Stokes equations. Zbl 1295.35354Guberovic, Rafaela; Schwab, Christoph; Stevenson, Rob 8 2014 Multilevel Monte Carlo finite element methods for stochastic elliptic variational inequalities. Zbl 1320.65176Kornhuber, Ralf; Schwab, Christoph; Wolf, Maren-Wanda 8 2014 Efficient resolution of anisotropic structures. Zbl 1317.65251Dahmen, Wolfgang; Huang, Chunyan; Kutyniok, Gitta; Lim, Wang-Q; Schwab, Christoph; Welper, Gerrit 7 2014 Optimality of adaptive Galerkin methods for random parabolic partial differential equations. Zbl 1293.35372Gittelson, Claude Jeffrey; Andreev, Roman; Schwab, Christoph 6 2014 High order SFV and mixed SDG/FV methods for the uncertainty quantification in multidimensional conservation laws. Zbl 1421.76164Tokareva, Svetlana; Schwab, Christoph; Mishra, Siddhartha 6 2014 Extraction of quantifiable information from complex systems. Zbl 1301.93005 1 2014 Sparse, adaptive Smolyak quadratures for Bayesian inverse problems. Zbl 1278.65008Schillings, Claudia; Schwab, Christoph 59 2013 Complexity analysis of accelerated MCMC methods for Bayesian inversion. Zbl 1288.65004Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M. 44 2013 Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs. Zbl 1273.65009Chkifa, Abdellah; Cohen, Albert; Devore, Ronald; Schwab, Christoph 40 2013 Computational methods for quantitative finance. Finite element methods for derivative pricing. Zbl 1275.91005Hilber, Norbert; Reichmann, Oleg; Schwab, Christoph; Winter, Christoph 30 2013 Multilevel Monte Carlo method for parabolic stochastic partial differential equations. Zbl 1272.65009Barth, Andrea; Lang, Annika; Schwab, Christoph 30 2013 ...and 192 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,325 Authors 169 Schwab, Christoph 57 Harbrecht, Helmut 48 Melenk, Jens Markus 42 Hiptmair, Ralf 42 Nobile, Fabio 38 Praetorius, Dirk 32 Tempone, Raúl F. 31 Demkowicz, Leszek F. 30 Schötzau, Dominik 30 Stevenson, Rob P. 27 Sauter, Stefan 26 Mishra, Siddhartha 25 Cohen, Albert 25 Schneider, Reinhold 25 Xenophontos, Christos A. 24 Cockburn, Bernardo 24 Houston, Paul 24 Wihler, Thomas Pascal 23 Abdulle, Assyr 22 Bespalov, Alexei 22 Dick, Josef 22 Multerer, Michael D. 22 Nouy, Anthony 22 Scheichl, Robert 21 Dolejší, Vít 21 Kuo, Frances Y. 21 Perugia, Ilaria 20 Dahmen, Wolfgang A. 20 Georgoulis, Emmanuil H. 19 Baccouch, Mahboub 19 Chen, Peng 19 Chernov, Alexey 19 Karniadakis, George Em 19 Khoromskiĭ, Boris Nikolaevich 19 Nicaise, Serge 19 Sloan, Ian Hugh 19 Süli, Endre E. 19 Yi, Lijun 18 Chung, Tsz Shun Eric 18 Feischl, Michael 18 Feistauer, Miloslav 18 Giani, Stefano 18 Hoang, Viet Ha 17 Li, Jichun 17 Marzouk, Youssef M. 17 Spence, Euan A. 17 Stephan, Ernst Peter 17 Urban, Karsten 17 Wheeler, Mary Fanett 16 Ainsworth, Mark 16 Ern, Alexandre 16 Hakula, Harri 16 Mascotto, Lorenzo 15 Antonietti, Paola Francesca 15 Bachmayr, Markus 15 Buffa, Annalisa 15 Goda, Takashi 15 Griebel, Michael 15 Heuer, Norbert 15 Jentzen, Arnulf 15 Narayan, Akil C. 15 Nuyens, Dirk 15 Rank, Ernst 15 Steinbach, Olaf 14 Barth, Andrea 14 Dahlke, Stephan 14 Düster, Alexander 14 Eigel, Martin 14 Führer, Thomas 14 Ghattas, Omar N. 14 Graham, Ivan G. 14 Karkulik, Michael 14 Shu, Chi-Wang 14 Verani, Marco 14 Zhang, Qiang 14 Zhang, Zhimin 13 Claeys, Xavier 13 DeVore, Ronald A. 13 Grohs, Philipp 13 Gunzburger, Max D. 13 Khan, Arbaz 13 Lang, Annika 13 Li, Hengguang 13 Matthies, Hermann Georg 13 Moiola, Andrea 13 Schöberl, Joachim 13 Webster, Clayton G. 12 Beuchler, Sven 12 Dinh Dũng 12 Dong, Zhaonan 12 Faustmann, Markus 12 Hackbusch, Wolfgang 12 Herrmann, Lukas 12 Jerez-Hanckes, Carlos 12 Kanschat, Guido 12 Kressner, Daniel 12 Law, Kody J. 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