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: 338 Publications since 1985, including 5 Books and 14 Additional arXiv Preprints 7 Contributions as Editor Software Indexed: 1 Package Co-Authors: 190 Co-Authors with 329 Joint Publications 4,606 Co-Co-Authors all top 5 Co-Authors 14 single-authored 24 Schötzau, Dominik 16 Melenk, Jens Markus 16 Zech, Jakob 15 Matache, Ana-Maria 14 Herrmann, Lukas 12 Mishra, Siddhartha 11 Marcati, Carlo 10 Gerdes, Klaus 10 Kuo, Frances Y. 10 Opschoor, Joost A. A. 10 Wendland, Wolfgang L. 9 Dick, Josef 9 von Petersdorff, Tobias 9 Wihler, Thomas Pascal 8 Harbrecht, Helmut 7 Chernov, Alexey 7 Cohen, Albert 7 Feistauer, Miloslav 7 Hiptmair, Ralf 7 Hoang, Viet Ha 7 Le Gia, Quoc Thong 7 Schneider, Reinhold 7 Sloan, Ian Hugh 7 Süli, Endre E. 6 Gantner, Robert Nicholas 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 Houston, Paul 5 Jerez-Hanckes, Carlos 5 Kazeev, Vladimir A. 5 Risebro, Nils Henrik 5 Schillings, Claudia 5 Toselli, Andrea 4 Andreev, Roman 4 Barth, Andrea 4 Dahmen, Wolfgang A. 4 Faustmann, Markus 4 Lang, Annika 4 Longo, Marcello 4 Müller, Fabian Lukas 4 Perugia, Ilaria 4 Stein, Andreas 4 Weber, Franziska 4 Winter, Christoph 3 Aylwin, Rubén 3 Banjai, Lehel 3 Bieri, Marcel 3 Buffa, Annalisa 3 Chen, Peng 3 Chkifa, Abdellah 3 DeVore, Ronald A. 3 Dinh Dũng 3 Dolejší, Vít 3 He, Yanchen 3 Henríquez, Fernando 3 Hilber, Norbert 3 Kirchner, Kristin 3 Petersen, Philipp Christian 3 Rakhuba, Maxim V. 3 Reich, Nils 3 Schmidlin, Gregor 3 Schulz, Heiko 3 Tokareva, Svetlana A. 3 Welper, Gerrit 2 Abdulle, Assyr 2 Beuchler, Sven 2 Braess, Dietrich 2 Cockburn, Bernardo 2 Costabel, Martin 2 Dauge, Monique 2 Demkowicz, Leszek 2 Eigel, Martin 2 Feischl, Michael 2 Frauenfelder, Philipp 2 Gonon, Lukas 2 Grella, Konstantin 2 Hackbusch, Wolfgang 2 Hansen, Markus 2 Huang, Chunyan 2 Humphrey, Jay D. 2 Koley, Ujjwal 2 Kozlov, Vladimir A. 2 Kunoth, Angela 2 Kutyniok, Gitta 2 Larsson, Stig 2 Lim, Wang-Q 2 Maz’ya, Vladimir Gilelevich 2 Moiola, Andrea 2 Oseledets, Ivan Valer’evich 2 Pentenrieder, Bastian 2 Quek, Jia Hao 2 Rauhut, Holger 2 Scheichl, Robert ...and 98 more Co-Authors all top 5 Serials 25 Numerische Mathematik 25 SIAM Journal on Numerical Analysis 19 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 9 IMA Journal of Numerical Analysis 8 Journal of Computational Physics 8 SIAM Journal on Scientific Computing 8 SIAM/ASA Journal on Uncertainty Quantification 7 SIAM Journal on Mathematical Analysis 6 Inverse Problems 6 Advances in Computational Mathematics 6 Foundations of Computational Mathematics 6 Analysis and Applications (Singapore) 5 Computers & Mathematics with Applications 5 Calcolo 4 BIT 4 Computing 4 Journal of Computational and Applied Mathematics 4 Applied Numerical 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 4 Stochastic and Partial Differential Equations. Analysis and Computations 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 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 of Functional Analysis 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 Neural Networks 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 Lecture Notes in Mathematics 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 271 Numerical analysis (65-XX) 180 Partial differential equations (35-XX) 74 Probability theory and stochastic processes (60-XX) 43 Fluid mechanics (76-XX) 31 Mechanics of deformable solids (74-XX) 28 Approximations and expansions (41-XX) 22 Computer science (68-XX) 15 Integral equations (45-XX) 15 Statistics (62-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Optics, electromagnetic theory (78-XX) 10 Operator theory (47-XX) 7 General and overarching topics; collections (00-XX) 7 Ordinary differential equations (34-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Real functions (26-XX) 6 Functions of a complex variable (30-XX) 6 Functional analysis (46-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Potential theory (31-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Classical thermodynamics, heat transfer (80-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 Global analysis, analysis on manifolds (58-XX) 2 Systems theory; control (93-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 308 Publications have been cited 8,699 times in 4,469 Documents Cited by ▼ Year ▼ \(p\)- and \(hp\)-finite element methods. Theory and applications in solid and fluid mechanics. Zbl 0910.73003 Schwab, Ch. 532 1998 Boundary element methods. Zbl 1215.65183 Sauter, Stefan A.; Schwab, Christoph 359 2011 Discontinuous \(hp\)-finite element methods for advection-diffusion-reaction problems. Zbl 1015.65067 Houston, Paul; Schwab, Christoph; Süli, Endre 249 2002 Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDE’s. Zbl 1219.35379 Cohen, Albert; DeVore, Ronald; Schwab, Christoph 180 2011 Karhunen-Loève approximation of random fields by generalized fast multipole methods. Zbl 1104.65008 Schwab, Christoph; Todor, Radu Alexandru 169 2006 Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs. Zbl 1206.60064 Cohen, Albert; DeVore, Ronald; Schwab, Christoph 168 2010 Finite elements for elliptic problems with stochastic coefficients. Zbl 1143.65392 Frauenfelder, Philipp; Schwab, Christoph; Todor, Radu Alexandru 167 2005 Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients. Zbl 1230.65006 Barth, Andrea; Schwab, Christoph; Zollinger, Nathaniel 165 2011 Optimal a priori error estimates for the \(hp\)-version of the local discontinuous Galerkin method for convection-diffusion problems. Zbl 0997.65111 Castillo, Paul; Cockburn, Bernardo; Schötzau, Dominik; Schwab, Christoph 158 2002 Local discontinuous Galerkin methods for the Stokes system. Zbl 1032.65127 Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik; Schwab, Christoph 155 2002 Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs. Zbl 1269.65010 Schwab, Christoph; Gittelson, Claude Jeffrey 135 2011 Quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients. Zbl 1271.65017 Kuo, Frances Y.; Schwab, Christoph; Sloan, Ian H. 128 2012 Time discretization of parabolic problems by the \(hp\)-version of the discontinuous Galerkin finite element method. Zbl 0978.65091 Schötzau, Dominik; Schwab, Christoph 111 2000 Space-time adaptive wavelet methods for parabolic evolution problems. Zbl 1198.65249 Schwab, Christoph; Stevenson, Rob 105 2009 Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients. Zbl 1120.65004 Todor, Radu Alexandru; Schwab, Christoph 99 2007 High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs. Zbl 1298.65022 Chkifa, Abdellah; Cohen, Albert; Schwab, Christoph 93 2014 Mixed hp-DGFEM for incompressible flows. Zbl 1055.76032 Schötzau, Dominik; Schwab, Christoph; Toselli, Andrea 92 2003 Tensor-structured Galerkin approximation of parametric and stochastic elliptic PDEs. Zbl 1243.65009 Khoromskij, Boris N.; Schwab, Christoph 88 2011 Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs. Zbl 1327.65251 Chkifa, Abdellah; Cohen, Albert; Schwab, Christoph 85 2015 Isotropic Gaussian random fields on the sphere: regularity, fast simulation and stochastic partial differential equations. Zbl 1328.60126 Lang, Annika; Schwab, Christoph 84 2015 The \(p\) and \(hp\) versions of the finite element method for problems with boundary layers. Zbl 0853.65115 Schwab, Christoph; Suri, Manil 83 1996 Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients. Zbl 1341.65003 Graham, I. G.; Kuo, F. Y.; Nichols, J. A.; Scheichl, R.; Schwab, Ch.; Sloan, I. H. 81 2015 Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data. Zbl 1271.65018 Mishra, Siddhartha; Schwab, Christoph 77 2012 Deep learning in high dimension: neural network expression rates for generalized polynomial chaos expansions in UQ. Zbl 1478.68309 Schwab, Christoph; Zech, Jakob 75 2019 An \(hp\) a priori error analysis of the DG time-stepping for initial value problems. Zbl 1012.65084 Schötzau, Dominik; Schwab, Christoph 73 2000 Sparse finite elements for elliptic problems with stochastic loading. Zbl 1044.65085 Schwab, Christoph; Todor, Radu-Alexandru 71 2003 Sparse, adaptive Smolyak quadratures for Bayesian inverse problems. Zbl 1278.65008 Schillings, Claudia; Schwab, Christoph 70 2013 Adaptive stochastic Galerkin FEM. Zbl 1296.65157 Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar 69 2014 Adaptive Petrov-Galerkin methods for first order transport equations. Zbl 1260.65091 Dahmen, Wolfgang; Huang, Chunyan; Schwab, Christoph; Welper, Gerrit 68 2012 Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions. Zbl 1402.76083 Mishra, S.; Schwab, Ch.; Šukys, J. 64 2012 Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs. Zbl 1326.65013 Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Nuyens, Dirk; Schwab, Christoph 63 2014 Sparse high order FEM for elliptic sPDEs. Zbl 1157.65481 Bieri, Marcel; Schwab, Christoph 62 2009 Boundary element methods for Maxwell transmission problems in Lipschitz domains. Zbl 1071.65160 Buffa, Annalisa; Hiptmair, Ralf; von Petersdorff, Tobias; Schwab, Christoph 60 2003 Stabilized \(hp\)-finite element methods for first-order hyperbolic problems. Zbl 0957.65103 Houston, Paul; Schwab, Christoph; Süli, Endre 58 2000 On numerical cubatures of singular surface integrals in boundary element methods. Zbl 0761.65012 Schwab, Christoph; Wendland, Wolfgang L. 57 1992 Sparse second moment analysis for elliptic problems in stochastic domains. Zbl 1146.65007 Harbrecht, Helmut; Schneider, Reinhold; Schwab, Christoph 57 2008 Numerical solution of parabolic equations in high dimensions. Zbl 1083.65095 von Petersdorff, Tobias; Schwab, Christoph 56 2004 Wavelet approximations for first kind boundary integral equations on polygons. Zbl 0863.65074 von Petersdorff, Tobias; Schwab, Christoph 55 1996 Fast deterministic pricing of options on Lévy driven assets. Zbl 1072.60052 Matache, Ana-Maria; von Petersdorff, Tobias; Schwab, Christoph 54 2004 Boundary element methods for Maxwell’s equations on non-smooth domains. Zbl 1019.65094 Buffa, Annalisa; Costabel, Martin; Schwab, Christoph 54 2002 Complexity analysis of accelerated MCMC methods for Bayesian inversion. Zbl 1288.65004 Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M. 54 2013 Sparse deterministic approximation of Bayesian inverse problems. Zbl 1236.62014 Schwab, C.; Stuart, A. M. 54 2012 Deep ReLU networks and high-order finite element methods. Zbl 1452.65354 Opschoor, Joost A. A.; Petersen, Philipp C.; Schwab, Christoph 54 2020 Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients. Zbl 1318.65006 Kuo, Frances Y.; Schwab, Christoph; Sloan, Ian H. 53 2015 High-dimensional finite elements for elliptic problems with multiple scales. Zbl 1074.65135 Viet Ha Hoang; Schwab, Christoph 51 2005 An adaptive wavelet method for solving high-dimensional elliptic PDEs. Zbl 1205.65313 Dijkema, Tammo Jan; Schwab, Christoph; Stevenson, Rob 51 2009 Fully discrete \(hp\)-finite elements: Fast quadrature. Zbl 0985.65141 Melenk, J. M.; Gerdes, K.; Schwab, Ch. 48 2001 Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs. Zbl 1273.65009 Chkifa, Abdellah; Cohen, Albert; Devore, Ronald; Schwab, Christoph 48 2013 Existence of global weak solutions for some polymeric flow models. Zbl 1161.76453 Barrett, John W.; Schwab, Christoph; Süli, Endre 46 2005 Sparse finite elements for stochastic elliptic problems — higher order moments. Zbl 1044.65006 Schwab, Ch.; Todor, R. A. 45 2003 Wavelet Galerkin pricing of American options on Lévy driven assets. Zbl 1134.91450 Matache, Ana-Maria; Nitsche, Pál-Andrej; Schwab, Christoph 45 2005 Sparse tensor discretization of elliptic SPDEs. Zbl 1205.35346 Bieri, Marcel; Andreev, Roman; Schwab, Christoph 45 2009 Quasi-Monte Carlo methods for high-dimensional integration: the standard (weighted Hilbert space) setting and beyond. Zbl 1248.65001 Kuo, F. Y.; Schwab, Ch.; Sloan, I. H. 45 2011 Multilevel quasi-Monte Carlo methods for lognormal diffusion problems. Zbl 1368.65005 Kuo, Frances Y.; Scheichl, Robert; Schwab, Christoph; Sloan, Ian H.; Ullmann, Elisabeth 44 2017 Fast numerical solution of parabolic integro-differential equations with applications in finance. Zbl 1098.65123 Matache, Ana-Maria; Schwab, Christoph; Wihler, Thomas P. 43 2005 Wavelet Galerkin algorithms for boundary integral equations. Zbl 0943.65134 Lage, Christian; Schwab, Christoph 41 1999 Kernel properties and representations of boundary integral operators. Zbl 0805.35168 Schwab, Christoph; Wendland, Wolfgang L. 40 1992 A posteriori modeling error estimation for hierarchic plate models. Zbl 0856.73031 Schwab, Christoph 40 1996 \(hp\)-discontinuous Galerkin time stepping for parabolic problems. Zbl 0992.65103 Werder, T.; Gerdes, K.; Schötzau, Dominik; Schwab, Christoph 40 2001 Computational methods for quantitative finance. Finite element methods for derivative pricing. Zbl 1275.91005 Hilber, Norbert; Reichmann, Oleg; Schwab, Christoph; Winter, Christoph 39 2013 DNN expression rate analysis of high-dimensional PDEs: application to option pricing. Zbl 1500.35009 Elbrächter, Dennis; Grohs, Philipp; Jentzen, Arnulf; Schwab, Christoph 39 2022 The \(hp\) finite element method for problems in mechanics with boundary layers. Zbl 0959.74073 Schwab, Christoph; Suri, Manil; Xenophontos, C. 38 1998 Analytic regularity and GPC approximation for control problems constrained by linear parametric elliptic and parabolic PDEs. Zbl 1278.49043 Kunoth, Angela; Schwab, Christoph 37 2013 Sparse finite element methods for operator equations with stochastic data. Zbl 1164.65300 von Petersdorff, Tobias; Schwab, Christoph 37 2006 Multilevel higher-order quasi-Monte Carlo Bayesian estimation. Zbl 1375.65169 Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph 36 2017 Boundary elements methods. Analysis, numerics and implementation of fast algorithms. (Randelementmethoden. Analyse, Numerik und Implementierung schneller Algorithmen.) Zbl 1059.65108 Sauter, Stefan; Schwab, Christoph 35 2004 Exponential convergence of \(hp\)-FEM for Maxwell equations with weighted regularization in polygonal domains. Zbl 1078.65089 Costabel, Martin; Dauge, Monique; Schwab, Christoph 35 2005 Multilevel Monte Carlo method for parabolic stochastic partial differential equations. Zbl 1272.65009 Barth, Andrea; Lang, Annika; Schwab, Christoph 35 2013 Large deformation shape uncertainty quantification in acoustic scattering. Zbl 1402.35321 Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch. 35 2018 Variable order composite quadrature of singular and nearly singular integrals. Zbl 0813.65057 Schwab, Christoph 33 1994 Tensor FEM for spectral fractional diffusion. Zbl 1429.65272 Banjai, Lehel; Melenk, Jens M.; Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.; Schwab, Christoph 33 2019 \(hp\)-dGFEM for second order elliptic problems in polyhedra. II: Exponential convergence. Zbl 1457.65215 Schötzau, D.; Schwab, Ch.; Wihler, T. P. 32 2013 Locking effects in the finite element approximation of plate models. Zbl 0827.73063 Suri, Manil; Babuška, Ivo; Schwab, Christoph 32 1995 A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes. Zbl 1335.65006 Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar 31 2015 Multiwavelets for second-kind integral equations. Zbl 0891.65121 Von Petersdorff, Tobias; Schwab, Christoph; Schneider, Reinhold 31 1997 Electromagnetic wave scattering by random surfaces: shape holomorphy. Zbl 1381.35170 Jerez-Hanckes, Carlos; Schwab, Christoph; Zech, Jakob 31 2017 Multilevel frames for sparse tensor product spaces. Zbl 1151.65010 Harbrecht, Helmut; Schneider, Reinhold; Schwab, Christoph 31 2008 Heterogeneous multiscale FEM for diffusion problems on rough surfaces. Zbl 1160.65337 Abdulle, Assyr; Schwab, Christoph 30 2005 \(N\)-term Wiener chaos approximation rates for elliptic PDEs with lognormal Gaussian random inputs. Zbl 1294.65010 Hoang, Viet Ha; Schwab, Christoph 30 2014 Hierarchic models for laminated plates and shells. Zbl 0959.74061 Actis, Ricardo L.; Szabo, Barna A.; Schwab, Christoph 30 1999 \(hp\) FEM for reaction-diffusion equations. I: Robust exponential convergence. Zbl 0972.65093 Melenk, Jens Markus; Schwab, Christoph 30 1998 Two-scale FEM for homogenization problems. Zbl 1070.65572 Matache, Ana-Maria; Schwab, Christoph 29 2002 Sparse-grid, reduced-basis Bayesian inversion. Zbl 1425.65020 Chen, Peng; Schwab, Christoph 29 2015 Analytic regularity of Stokes flow on polygonal domains in countably weighted Sobolev spaces. Zbl 1121.35098 Guo, Benqi; Schwab, Christoph 29 2006 Quadrature for \(hp\)-Galerkin BEM in \(\mathbb{R}^3\). Zbl 0901.65069 Sauter, Stefan A.; Schwab, Christoph 29 1997 Exponential ReLU DNN expression of holomorphic maps in high dimension. Zbl 1500.41008 Opschoor, J. A. A.; Schwab, Ch.; Zech, J. 29 2022 Higher order quasi-Monte Carlo integration for holomorphic, parametric operator equations. Zbl 1398.65031 Dick, Josef; Le Gia, Quoc T.; Schwab, Christoph 29 2016 Numerical solution of scalar conservation laws with random flux functions. Zbl 1343.65007 Mishra, Siddhartha; Risebro, Nils Henrik; Schwab, Christoph; Tokareva, Svetlana 28 2016 Exponential convergence of {\(hp\)} quadrature for integral operators with Gevrey kernels. Zbl 1269.65143 Chernov, Alexey; Von Petersdorff, Tobias; Schwab, Christoph 28 2011 Multilevel higher order QMC Petrov-Galerkin discretization for affine parametric operator equations. Zbl 1347.65012 Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph 28 2016 Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions. Zbl 1382.65409 Kazeev, Vladimir; Schwab, Christoph 28 2018 Sparsity in Bayesian inversion of parametric operator equations. Zbl 1291.65033 Schillings, Claudia; Schwab, Christoph 27 2014 Natural boundary element methods for the electric field integral equation on polyhedra. Zbl 1010.78014 Hiptmair, Ralf; Schwab, Christoph 27 2002 A finite volume discontinuous Galerkin scheme for nonlinear convection-diffusion problems. Zbl 1098.65095 Dolejší, Vít; Feistauer, Miloslav; Schwab, Christoph 27 2002 Sparse-grid, reduced-basis Bayesian inversion: nonaffine-parametric nonlinear equations. Zbl 1349.62076 Chen, Peng; Schwab, Christoph 27 2016 On some aspects of the discontinuous Galerkin finite element method for conservation laws. Zbl 1013.65108 Dolejší, Vít; Feistauer, Miloslav; Schwab, Christoph 26 2003 Numerical methods for Lévy processes. Zbl 1195.91175 Hilber, N.; Reich, N.; Schwab, C.; Winter, C. 26 2009 Sparse adaptive finite elements for radiative transfer. Zbl 1147.65095 Widmer, G.; Hiptmair, R.; Schwab, Ch. 26 2008 Shape holomorphy of the stationary Navier-Stokes equations. Zbl 1390.35227 Cohen, Albert; Schwab, Christoph; Zech, Jakob 26 2018 Fourier mode analysis of layers in shallow shell deformations. Zbl 0983.74039 Pitkäranta, Juhani; Matache, Ana-Maria; Schwab, Christoph 25 2001 The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs. Zbl 1541.35034 Harbrecht, Helmut; Schmidlin, Marc; Schwab, Christoph 1 2024 Analytic regularity and solution approximation for a semilinear elliptic partial differential equation in a polygon. Zbl 1534.35169 He, Yanchen; Schwab, Christoph 1 2024 Multilevel Monte Carlo FEM for elliptic PDEs with Besov random tree priors. Zbl 07914045 Schwab, Christoph; Stein, Andreas 1 2024 Exponential ReLU neural network approximation rates for point and edge singularities. Zbl 1519.35253 Marcati, Carlo; Opschoor, Joost A. A.; Petersen, Philipp C.; Schwab, Christoph 9 2023 Deep ReLU neural networks overcome the curse of dimensionality for partial integrodifferential equations. Zbl 07652560 Gonon, Lukas; Schwab, Christoph 8 2023 Exponential convergence of deep operator networks for elliptic partial differential equations. Zbl 1519.35088 Marcati, Carlo; Schwab, Christoph 6 2023 Exponential convergence of hp FEM for spectral fractional diffusion in polygons. Zbl 1511.65117 Banjai, Lehel; Melenk, Jens M.; Schwab, Christoph 2 2023 Exponential convergence of \(hp\)-time-stepping in space-time discretizations of parabolic PDEs. Zbl 1516.65097 Perugia, Ilaria; Schwab, Christoph; Zank, Marco 2 2023 Deep learning in high dimension: neural network expression rates for analytic functions in \(L^2(\mathbb{R}^d,\gamma_d)\). Zbl 1524.41084 Schwab, Christoph; Zech, Jakob 2 2023 De Rham compatible deep neural network FEM. Zbl 1532.65083 Longo, Marcello; Opschoor, Joost A. A.; Disch, Nico; Schwab, Christoph; Zech, Jakob 2 2023 ReLU neural network Galerkin BEM. Zbl 07698915 Aylwin, Rubén; Henríquez, Fernando; Schwab, Christoph 1 2023 \(hp\)-FEM for reaction-diffusion equations. II: Robust exponential convergence for multiple length scales in corner domains. Zbl 1537.65165 Banjai, Lehel; Melenk, Jens M.; Schwab, Christoph 1 2023 DNN expression rate analysis of high-dimensional PDEs: application to option pricing. Zbl 1500.35009 Elbrächter, Dennis; Grohs, Philipp; Jentzen, Arnulf; Schwab, Christoph 39 2022 Exponential ReLU DNN expression of holomorphic maps in high dimension. Zbl 1500.41008 Opschoor, J. A. A.; Schwab, Ch.; Zech, J. 29 2022 Constructive deep ReLU neural network approximation. Zbl 1500.41002 Herrmann, Lukas; Opschoor, Joost A. A.; Schwab, Christoph 7 2022 Weighted analytic regularity for the integral fractional Laplacian in polygons. Zbl 1505.35070 Faustmann, Markus; Marcati, Carlo; Melenk, Jens Markus; Schwab, Christoph 6 2022 Tensor rank bounds for point singularities in \(\mathbb{R}^3\). Zbl 1487.35019 Marcati, C.; Rakhuba, M.; Schwab, Ch. 5 2022 Quantized tensor FEM for multiscale problems: diffusion problems in two and three dimensions. Zbl 1496.65220 Kazeev, Vladimir; Oseledets, Ivan; Rakhuba, Maxim V.; Schwab, Christoph 4 2022 Deep learning in high dimension: ReLU neural network expression for Bayesian PDE inversion. Zbl 1487.68200 Opschoor, Joost A. A.; Schwab, Christoph; Zech, Jakob 2 2022 Extrapolated polynomial lattice rule integration in computational uncertainty quantification. Zbl 1494.65004 Dick, Josef; Longo, Marcello; Schwab, Christoph 1 2022 Deep solution operators for variational inequalities via proximal neural networks. Zbl 07546269 Schwab, Christoph; Stein, Andreas 1 2022 Space-time discontinuous Galerkin approximation of acoustic waves with point singularities. Zbl 07528299 Bansal, Pratyuksh; Moiola, Andrea; Perugia, Ilaria; Schwab, Christoph 12 2021 Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models. Zbl 1475.91356 Gonon, Lukas; Schwab, Christoph 12 2021 Higher-order quasi-Monte Carlo training of deep neural networks. Zbl 1492.65043 Longo, Marcello; Mishra, Siddhartha; Rusch, T. Konstantin; Schwab, Christoph 7 2021 Shape holomorphy of the Calderón projector for the Laplacian in \(\mathbb{R}^2\). Zbl 1472.45011 Henríquez, Fernando; Schwab, Christoph 6 2021 Exponential convergence of mixed \(hp\)-DGFEM for the incompressible Navier-Stokes equations in \(\mathbb{R}^2\). Zbl 1519.65057 Schötzau, Dominik; Marcati, Carlo; Schwab, Christoph 3 2021 Multilevel Markov chain Monte Carlo for Bayesian inversion of parabolic partial differential equations under Gaussian prior. Zbl 1465.65006 Hoang, Viet Ha; Quek, Jia Hao; Schwab, Christoph 3 2021 Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems. Zbl 1478.65107 Herrmann, Lukas; Keller, Magdalena; Schwab, Christoph 3 2021 Deep ReLU networks and high-order finite element methods. Zbl 1452.65354 Opschoor, Joost A. A.; Petersen, Philipp C.; Schwab, Christoph 54 2020 Convergence rates of high dimensional Smolyak quadrature. Zbl 07240638 Zech, Jakob; Schwab, Christoph 22 2020 Deep neural network expression of posterior expectations in Bayesian PDE inversion. Zbl 1453.35191 Herrmann, Lukas; Schwab, Christoph; Zech, Jakob 17 2020 Multilevel approximation of Gaussian random fields: fast simulation. Zbl 1448.60110 Herrmann, Lukas; Kirchner, Kristin; Schwab, Christoph 13 2020 Domain uncertainty quantification in computational electromagnetics. Zbl 1483.65010 Aylwin, Ruben; Jerez-Hanckes, Carlos; Schwab, Christoph; Zech, Jakob 11 2020 Analysis of a multilevel Markov chain Monte Carlo finite element method for Bayesian inversion of log-normal diffusions. Zbl 1491.65010 Hoang, Viet Ha; Quek, Jia Hao; Schwab, Christoph 7 2020 Analytic regularity for the incompressible Navier-Stokes equations in polygons. Zbl 1447.35252 Marcati, Carlo; Schwab, Christoph 5 2020 Exponential convergence in \(H^1\) of hp-FEM for Gevrey regularity with isotropic singularities. Zbl 1433.65290 Feischl, M.; Schwab, Ch. 5 2020 Multilevel quasi-Monte Carlo uncertainty quantification for advection-diffusion-reaction. Zbl 07240088 Herrmann, Lukas; Schwab, Christoph 4 2020 Spectral and high order methods for partial differential equations, ICOSAHOM 2018. Selected papers from the ICOSAHOM conference, London, UK, July 9–13, 2018. Zbl 1462.65006 2 2020 Deep learning in high dimension: neural network expression rates for generalized polynomial chaos expansions in UQ. Zbl 1478.68309 Schwab, Christoph; Zech, Jakob 75 2019 Tensor FEM for spectral fractional diffusion. Zbl 1429.65272 Banjai, Lehel; Melenk, Jens M.; Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.; Schwab, Christoph 33 2019 Higher order quasi-Monte Carlo integration for Bayesian PDE inversion. Zbl 1442.62051 Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph 19 2019 Multilevel quasi-Monte Carlo integration with product weights for elliptic PDEs with lognormal coefficients. Zbl 07135561 Herrmann, Lukas; Schwab, Christoph 18 2019 Multilevel approximation of parametric and stochastic PDES. Zbl 1427.65386 Zech, Jakob; Dũng, Dinh; Schwab, Christoph 16 2019 QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights. Zbl 07006664 Herrmann, Lukas; Schwab, Christoph 14 2019 Improved efficiency of a multi-index FEM for computational uncertainty quantification. Zbl 07100359 Dick, Josef; Feischl, Michael; Schwab, Christoph 5 2019 Uncertainty quantification for spectral fractional diffusion: sparsity analysis of parametric solutions. Zbl 1469.65170 Herrmann, Lukas; Schwab, Christoph; Zech, Jakob 2 2019 Large deformation shape uncertainty quantification in acoustic scattering. Zbl 1402.35321 Hiptmair, R.; Scarabosio, L.; Schillings, C.; Schwab, Ch. 35 2018 Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions. Zbl 1382.65409 Kazeev, Vladimir; Schwab, Christoph 28 2018 Shape holomorphy of the stationary Navier-Stokes equations. Zbl 1390.35227 Cohen, Albert; Schwab, Christoph; Zech, Jakob 26 2018 Quasi-Monte Carlo integration for affine-parametric, elliptic PDEs: local supports and product weights. Zbl 1378.65072 Gantner, Robert N.; Herrmann, Lukas; Schwab, Christoph 17 2018 Numerical analysis of lognormal diffusions on the sphere. Zbl 1402.60062 Herrmann, Lukas; Lang, Annika; Schwab, Christoph 12 2018 Space-time \(hp\)-approximation of parabolic equations. Zbl 1404.65118 Devaud, Denis; Schwab, Christoph 11 2018 Multilevel QMC with product weights for affine-parametric, elliptic PDEs. Zbl 1405.65008 Gantner, Robert N.; Herrmann, Lukas; Schwab, Christoph 11 2018 Adaptive anisotropic Petrov-Galerkin methods for first order transport equations. Zbl 1435.65197 Dahmen, Wolfgang; Kutyniok, Gitta; Lim, Wang-Q; Schwab, Christoph; Welper, Gerrit 7 2018 Exponential convergence of \(hp\)-FEM for elliptic problems in polyhedra: mixed boundary conditions and anisotropic polynomial degrees. Zbl 1402.65166 Schötzau, Dominik; Schwab, Christoph 7 2018 QMC algorithms with product weights for lognormal-parametric, elliptic PDEs. Zbl 1422.65017 Herrmann, Lukas; Schwab, Christoph 7 2018 Discontinuous Galerkin methods for acoustic wave propagation in polygons. Zbl 1406.65080 Müller, Fabian; Schötzau, Dominik; Schwab, Christoph 6 2018 Correction to: “Multilevel Monte Carlo front-tracking for random scalar conservation laws”. Zbl 1430.65004 Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska 1 2018 Multilevel quasi-Monte Carlo methods for lognormal diffusion problems. Zbl 1368.65005 Kuo, Frances Y.; Scheichl, Robert; Schwab, Christoph; Sloan, Ian H.; Ullmann, Elisabeth 44 2017 Multilevel higher-order quasi-Monte Carlo Bayesian estimation. Zbl 1375.65169 Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph 36 2017 Electromagnetic wave scattering by random surfaces: shape holomorphy. Zbl 1381.35170 Jerez-Hanckes, Carlos; Schwab, Christoph; Zech, Jakob 31 2017 Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations. Zbl 1358.65034 Rauhut, Holger; Schwab, Christoph 25 2017 Fully discrete approximation of parametric and stochastic elliptic PDEs. Zbl 1377.65005 Bachmayr, Markus; Cohen, Albert; Dũng, Dinh; Schwab, Christoph 21 2017 Covariance regularity and \(\mathcal {H}\)-matrix approximation for rough random fields. Zbl 1362.65124 Dölz, J.; Harbrecht, H.; Schwab, Ch. 18 2017 A multilevel Monte Carlo finite difference method for random scalar degenerate convection-diffusion equations. Zbl 1373.35179 Koley, Ujjwal; Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska 17 2017 Fractional space-time variational formulations of (Navier-) Stokes equations. Zbl 1375.35329 Schwab, Christoph; Stevenson, Rob 13 2017 Electromagnetic wave scattering by random surfaces: uncertainty quantification via sparse tensor boundary elements. Zbl 1433.78013 Jerez-Hanckes, Carlos; Schwab, Christoph 12 2017 QTT-finite-element approximation for multiscale problems. I: Model problems in one dimension. Zbl 1375.65152 Kazeev, Vladimir; Oseledets, Ivan; Rakhuba, Maxim; Schwab, Christoph 12 2017 Symmetric interior penalty discontinuous Galerkin methods for elliptic problems in polygons. Zbl 1376.65145 Müller, Fabian; Schötzau, Dominik; Schwab, Christoph 5 2017 Monte-Carlo finite-volume methods in uncertainty quantification for hyperbolic conservation laws. Zbl 1407.65150 Mishra, Siddhartha; Schwab, Christoph 5 2017 Higher order quasi-Monte Carlo integration for holomorphic, parametric operator equations. Zbl 1398.65031 Dick, Josef; Le Gia, Quoc T.; Schwab, Christoph 29 2016 Numerical solution of scalar conservation laws with random flux functions. Zbl 1343.65007 Mishra, Siddhartha; Risebro, Nils Henrik; Schwab, Christoph; Tokareva, Svetlana 28 2016 Multilevel higher order QMC Petrov-Galerkin discretization for affine parametric operator equations. Zbl 1347.65012 Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph 28 2016 Sparse-grid, reduced-basis Bayesian inversion: nonaffine-parametric nonlinear equations. Zbl 1349.62076 Chen, Peng; Schwab, Christoph 27 2016 Scaling limits in computational Bayesian inversion. Zbl 1358.65013 Schillings, Claudia; Schwab, Christoph 25 2016 Computational higher order quasi-Monte Carlo integration. Zbl 1356.65003 Gantner, Robert N.; Schwab, Christoph 24 2016 Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium. Zbl 1351.76117 Mishra, S.; Schwab, Ch.; Šukys, J. 18 2016 Adaptive sparse grid model order reduction for fast Bayesian estimation and inversion. Zbl 1337.65012 Chen, Peng; Schwab, Christoph 17 2016 Sparse adaptive tensor Galerkin approximations of stochastic PDE-constrained control problems. Zbl 1398.65252 Kunoth, Angela; Schwab, Christoph 14 2016 \(hp\)-dGFEM for second-order mixed elliptic problems in polyhedra. Zbl 1332.65173 Schötzau, Dominik; Schwab, Christoph; Wihler, Thomas P. 11 2016 Finite elements with mesh refinement for elastic wave propagation in polygons. Zbl 1457.65130 Müller, Fabian; Schwab, Christoph 10 2016 Multilevel Monte Carlo front-tracking for random scalar conservation laws. Zbl 1350.65008 Risebro, Nils Henrik; Schwab, Christoph; Weber, Franziska 7 2016 Numerical approximation of statistical solutions of planar, incompressible flows. Zbl 1416.76184 Leonardi, Filippo; Mishra, Siddhartha; Schwab, Christoph 5 2016 Multilevel Monte Carlo simulation of statistical solutions to the Navier-Stokes equations. Zbl 1382.76209 Barth, Andrea; Schwab, Christoph; Šukys, Jonas 2 2016 Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs. Zbl 1327.65251 Chkifa, Abdellah; Cohen, Albert; Schwab, Christoph 85 2015 Isotropic Gaussian random fields on the sphere: regularity, fast simulation and stochastic partial differential equations. Zbl 1328.60126 Lang, Annika; Schwab, Christoph 84 2015 Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients. Zbl 1341.65003 Graham, I. G.; Kuo, F. Y.; Nichols, J. A.; Scheichl, R.; Schwab, Ch.; Sloan, I. H. 81 2015 Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients. Zbl 1318.65006 Kuo, Frances Y.; Schwab, Christoph; Sloan, Ian H. 53 2015 A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes. Zbl 1335.65006 Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar 31 2015 Sparse-grid, reduced-basis Bayesian inversion. Zbl 1425.65020 Chen, Peng; Schwab, Christoph 29 2015 Finite elements with mesh refinement for wave equations in polygons. Zbl 1311.65126 Müller, Fabian L.; Schwab, Christoph 14 2015 Exponential convergence for \(hp\)-version and spectral finite element methods for elliptic problems in polyhedra. Zbl 1322.65099 Schötzau, Dominik; Schwab, Christoph 10 2015 Tensor approximation of stationary distributions of chemical reaction networks. Zbl 1322.60155 Kazeev, Vladimir; Schwab, Christoph 9 2015 Fast QMC matrix-vector multiplication. Zbl 1320.65008 Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Schwab, Christoph 6 2015 Quadrature algorithms for high dimensional singular integrands on simplices. Zbl 1332.65035 Chernov, Alexey; von Petersdorff, Tobias; Schwab, Christoph 5 2015 Exponential convergence of simplicial hp-FEM for \(H^1\)-functions with isotropic singularities. Zbl 1352.65548 Schwab, Christoph 1 2015 Higher order quasi Monte-Carlo integration in uncertainty quantification. Zbl 1352.65017 Dick, Josef; Thong Le Gia, Quoc; Schwab, Christoph 1 2015 High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs. Zbl 1298.65022 Chkifa, Abdellah; Cohen, Albert; Schwab, Christoph 93 2014 Adaptive stochastic Galerkin FEM. Zbl 1296.65157 Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar 69 2014 Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs. Zbl 1326.65013 Dick, Josef; Kuo, Frances Y.; Le Gia, Quoc T.; Nuyens, Dirk; Schwab, Christoph 63 2014 ...and 208 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,033 Authors 182 Schwab, Christoph 65 Harbrecht, Helmut 53 Melenk, Jens Markus 45 Nobile, Fabio 43 Hiptmair, Ralf 41 Praetorius, Dirk 35 Demkowicz, Leszek 35 Tempone, Raúl F. 31 Sauter, Stefan 30 Schötzau, Dominik 30 Stevenson, Rob P. 29 Mishra, Siddhartha 29 Xenophontos, Christos A. 28 Wihler, Thomas Pascal 27 Cohen, Albert 27 Dolejší, Vít 27 Scheichl, Robert 26 Houston, Paul 26 Schneider, Reinhold 25 Kuo, Frances Y. 24 Cockburn, Bernardo 24 Multerer, Michael D. 23 Dick, Josef 23 Hakula, Harri 23 Khoromskiĭ, Boris Nikolaevich 23 Nouy, Anthony 23 Perugia, Ilaria 23 Sloan, Ian Hugh 23 Süli, Endre E. 22 Abdulle, Assyr 22 Bespalov, Alexei 22 Dahmen, Wolfgang A. 22 Giani, Stefano 22 Yi, Lijun 21 Ainsworth, Mark 21 Chen, Peng 21 Karniadakis, George Em 20 Antonietti, Paola Francesca 20 Baccouch, Mahboub 20 Chernov, Alexey 20 Claeys, Xavier 20 Feischl, Michael 20 Georgoulis, Emmanuil H. 20 Jentzen, Arnulf 20 Mascotto, Lorenzo 20 Nicaise, Serge 19 Chung, Tsz Shun Eric 19 Spence, Euan A. 18 Feistauer, Miloslav 18 Hoang, Viet Ha 18 Kressner, Daniel 18 Marzouk, Youssef M. 18 Steinbach, Olaf 18 Stephan, Ernst Peter 18 Urban, Karsten 17 Führer, Thomas 17 Heuer, Norbert 17 Lang, Annika 17 Li, Jichun 17 Wheeler, Mary Fanett 16 Bachmayr, Markus 16 Barth, Andrea 16 Dahlke, Stephan 16 Ern, Alexandre 16 Ghattas, Omar N. 16 Goda, Takashi 16 Griebel, Michael 16 Herrmann, Lukas 16 Jerez-Hanckes, Carlos 16 Karkulik, Michael 16 Nuyens, Dirk 16 Rank, Ernst 16 Schöberl, Joachim 15 Beuchler, Sven 15 Buffa, Annalisa 15 Eigel, Martin 15 Moiola, Andrea 15 Narayan, Akil C. 15 Nochetto, Ricardo Horacio 15 Shu, Chi-Wang 15 Verani, Marco 15 Zech, Jakob 15 Zhang, Qiang 15 Zhang, Zhimin 14 DeVore, Ronald A. 14 Dinh Dũng 14 Dolgov, Sergey V. 14 Düster, Alexander 14 Dutt, Pravir Kumar 14 Faustmann, Markus 14 Graham, Ivan G. 14 Khan, Arbaz 14 Law, Kody J. H. 14 Li, Hengguang 14 Matthies, Hermann Georg 14 Tamellini, Lorenzo 14 Webster, Clayton G. 14 Zhang, Shangyou 13 Dölz, Jürgen 13 Grohs, Philipp ...and 4,933 more Authors all top 5 Cited in 371 Serials 395 Computer Methods in Applied Mechanics and Engineering 312 Journal of Computational Physics 212 Journal of Scientific Computing 187 Computers & Mathematics with Applications 179 Journal of Computational and Applied Mathematics 179 Numerische Mathematik 163 SIAM Journal on Scientific Computing 136 Applied Numerical Mathematics 125 Mathematics of Computation 113 SIAM Journal on Numerical Analysis 102 SIAM/ASA Journal on Uncertainty Quantification 87 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 78 International Journal for Numerical Methods in Engineering 75 Applied Mathematics and Computation 74 Advances in Computational Mathematics 66 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 56 Engineering Analysis with Boundary Elements 49 Numerical Methods for Partial Differential Equations 43 Computational Methods in Applied Mathematics 40 BIT 37 Mathematical Methods in the Applied Sciences 35 Journal of Complexity 34 Mathematics and Computers in Simulation 33 Computers and Fluids 33 Numerical Linear Algebra with Applications 33 Foundations of Computational Mathematics 32 Multiscale Modeling & Simulation 31 Computational Mechanics 29 Journal of Mathematical Analysis and Applications 28 Constructive Approximation 28 Numerical Algorithms 26 Calcolo 25 Journal of Numerical Mathematics 24 SIAM Journal on Mathematical Analysis 24 Communications in Computational Physics 23 Inverse Problems 23 International Journal of Computer Mathematics 20 Journal of Approximation Theory 20 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 19 Journal of Integral Equations and Applications 19 Computational and Applied Mathematics 18 Applicable Analysis 18 International Journal of Numerical Analysis and Modeling 18 Stochastic and Partial Differential Equations. Analysis and Computations 16 Computing 16 Numerical Functional Analysis and Optimization 16 Applications of Mathematics 16 Analysis and Applications (Singapore) 15 Computing and Visualization in Science 15 Computational Geosciences 14 Applied Mathematical Modelling 14 Applied and Computational Harmonic Analysis 13 Integral Equations and Operator Theory 13 Acta Numerica 13 Science China. Mathematics 13 Communications on Applied Mathematics and Computation 11 Journal of Differential Equations 11 Finance and Stochastics 11 Comptes Rendus. Mathématique. Académie des Sciences, Paris 11 Statistics and Computing 10 SIAM Review 10 Stochastic Processes and their Applications 10 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 10 Archives of Computational Methods in Engineering 9 Archive for Rational Mechanics and Analysis 9 International Journal for Numerical Methods in Fluids 9 Communications in Numerical Methods in Engineering 9 Vietnam Journal of Mathematics 9 Quantitative Finance 9 International Journal of Computational Methods 9 Oberwolfach Reports 9 Discrete and Continuous Dynamical Systems. Series S 8 Applied Mathematics Letters 8 SIAM Journal on Applied Mathematics 8 Computational Optimization and Applications 8 ETNA. Electronic Transactions on Numerical Analysis 8 Bernoulli 8 International Journal of Theoretical and Applied Finance 8 Discrete and Continuous Dynamical Systems. Series B 8 Journal of Applied Mathematics and Computing 8 SN Partial Differential Equations and Applications 7 Computer Physics Communications 7 Neural Networks 7 The Annals of Applied Probability 7 Journal of Elasticity 7 Journal de Mathématiques Pures et Appliquées. Neuvième Série 7 Linear Algebra and its Applications 6 Journal of Fluid Mechanics 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 ACM Transactions on Mathematical Software 6 SIAM Journal on Control and Optimization 6 Mathematical and Computer Modelling 6 SIAM Journal on Matrix Analysis and Applications 6 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 5 Communications in Mathematical Physics 5 Journal of Engineering Mathematics 5 Nonlinearity 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 Continuum Mechanics and Thermodynamics ...and 271 more Serials all top 5 Cited in 49 Fields 3,519 Numerical analysis (65-XX) 1,918 Partial differential equations (35-XX) 724 Fluid mechanics (76-XX) 590 Probability theory and stochastic processes (60-XX) 484 Mechanics of deformable solids (74-XX) 285 Approximations and expansions (41-XX) 258 Optics, electromagnetic theory (78-XX) 245 Statistics (62-XX) 203 Computer science (68-XX) 181 Calculus of variations and optimal control; optimization (49-XX) 155 Integral equations (45-XX) 149 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 106 Harmonic analysis on Euclidean spaces (42-XX) 100 Linear and multilinear algebra; matrix theory (15-XX) 98 Operator theory (47-XX) 92 Functional analysis (46-XX) 85 Statistical mechanics, structure of matter (82-XX) 76 Biology and other natural sciences (92-XX) 65 Operations research, mathematical programming (90-XX) 61 Systems theory; control (93-XX) 56 Ordinary differential equations (34-XX) 47 Geophysics (86-XX) 40 Real functions (26-XX) 39 Potential theory (31-XX) 33 Special functions (33-XX) 33 Classical thermodynamics, heat transfer (80-XX) 31 Information and communication theory, circuits (94-XX) 25 Quantum theory (81-XX) 22 Global analysis, analysis on manifolds (58-XX) 20 Dynamical systems and ergodic theory (37-XX) 11 General and overarching topics; collections (00-XX) 11 Number theory (11-XX) 11 Functions of a complex variable (30-XX) 10 Several complex variables and analytic spaces (32-XX) 10 Astronomy and astrophysics (85-XX) 9 Integral transforms, operational calculus (44-XX) 8 Measure and integration (28-XX) 6 Abstract harmonic analysis (43-XX) 6 Relativity and gravitational theory (83-XX) 4 Combinatorics (05-XX) 3 Differential geometry (53-XX) 3 Mechanics of particles and systems (70-XX) 2 History and biography (01-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 2 Manifolds and cell complexes (57-XX) 2 Mathematics education (97-XX) 1 Field theory and polynomials (12-XX) 1 Sequences, series, summability (40-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.