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ORCIDChristoph Schwab
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- affiliation: ETH Zurich, Switzerland
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2020 – today
- 2024
[j123]Lukas Herrmann
, Christoph Schwab, Jakob Zech:
Neural and spectral operator surrogates: unified construction and expression rate bounds. Adv. Comput. Math. 50(4): 72 (2024)- [j122]Helmut Harbrecht, Lukas Herrmann, Kristin Kirchner, Christoph Schwab:
Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction. Adv. Comput. Math. 50(5): 101 (2024) - [j121]Joost A. A. Opschoor, Christoph Schwab:
Deep ReLU networks and high-order finite element methods II: Chebyšev emulation. Comput. Math. Appl. 169: 142-162 (2024) - [j120]Helmut Harbrecht, Michael D. Multerer, Olaf Schenk, Christoph Schwab:
Multiresolution kernel matrix algebra. Numerische Mathematik 156(3): 1085-1114 (2024) - [j119]Yanchen He, Carlo Marcati, Christoph Schwab:
Analytic Regularity of Solutions to the Navier-Stokes Equations with Mixed Boundary Conditions in Polygons. SIAM J. Math. Anal. 56(2): 2488-2520 (2024) - [i36]Joost A. A. Opschoor, Christoph Schwab, Christos Xenophontos:
Neural Networks for Singular Perturbations. CoRR abs/2401.06656 (2024) - [i35]Helmut Harbrecht, Christoph Schwab, Marco Zank:
Wavelet compressed, modified Hilbert transform in the space-time discretization of the heat equation. CoRR abs/2402.10346 (2024) - [i34]Joost A. A. Opschoor, Christoph Schwab:
Exponential Expressivity of ReLUk Neural Networks on Gevrey Classes with Point Singularities. CoRR abs/2403.02035 (2024) - [i33]Yanchen He, Paul Houston, Christoph Schwab, Thomas P. Wihler:
Exponential Convergence of hp-ILGFEM for semilinear elliptic boundary value problems with monomial reaction. CoRR abs/2404.18569 (2024) - [i32]Fernando Henríquez, Christoph Schwab:
Deep ReLU Neural Network Emulation in High-Frequency Acoustic Scattering. CoRR abs/2405.12624 (2024) - [i31]Ralf Hiptmair, Christoph Schwab, Euan A. Spence:
Frequency-Explicit Shape Holomorphy in Uncertainty Quantification for Acoustic Scattering. CoRR abs/2408.01194 (2024) - [i30]Joost A. A. Opschoor, Philipp Christian Petersen, Christoph Schwab:
First Order System Least Squares Neural Networks. CoRR abs/2409.20264 (2024) - 2023
- [j118]Carlo Marcati, Joost A. A. Opschoor, Philipp Christian Petersen, Christoph Schwab:
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities. Found. Comput. Math. 23(3): 1043-1127 (2023) - [j117]Rubén Aylwin, Fernando Henríquez, Christoph Schwab:
ReLU Neural Network Galerkin BEM. J. Sci. Comput. 95(2): 41 (2023) - [j116]Christoph Schwab, Jakob Zech:
Deep Learning in High Dimension: Neural Network Expression Rates for Analytic Functions in \(\pmb{L^2(\mathbb{R}^d,\gamma_d)}\). SIAM/ASA J. Uncertain. Quantification 11(1): 199-234 (2023) - [j115]Lehel Banjai, Jens Markus Melenk, Christoph Schwab:
Exponential convergence of hp FEM for spectral fractional diffusion in polygons. Numerische Mathematik 153(1): 1-47 (2023) - [j114]Marcello Longo, Joost A. A. Opschoor, Nico Disch, Christoph Schwab, Jakob Zech:
De Rham compatible Deep Neural Network FEM. Neural Networks 165: 721-739 (2023) - [j113]Carlo Marcati, Christoph Schwab:
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations. SIAM J. Numer. Anal. 61(3): 1513-1545 (2023) - [j112]Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab:
Exponential Convergence of \(hp\)-FEM for the Integral Fractional Laplacian in Polygons. SIAM J. Numer. Anal. 61(6): 2601-2622 (2023) - [i29]Marcello Longo, Christoph Schwab, Andreas Stein:
A-posteriori QMC-FEM error estimation for Bayesian inversion and optimal control with entropic risk measure. CoRR abs/2301.03327 (2023) - [i28]Christoph Schwab, Andreas Stein:
Multilevel Monte Carlo FEM for Elliptic PDEs with Besov Random Tree Priors. CoRR abs/2302.00522 (2023) - [i27]Christoph Schwab, Andreas Stein, Jakob Zech:
Deep Operator Network Approximation Rates for Lipschitz Operators. CoRR abs/2307.09835 (2023) - [i26]Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab:
Weighted analytic regularity for the integral fractional Laplacian in polyhedra. CoRR abs/2307.11679 (2023) - [i25]Helmut Harbrecht, Marc Schmidlin, Christoph Schwab:
The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs. CoRR abs/2310.01256 (2023) - [i24]Joost A. A. Opschoor, Christoph Schwab:
Deep ReLU networks and high-order finite element methods II: Chebyshev emulation. CoRR abs/2310.07261 (2023) - 2022
- [j111]Carlo Marcati, Maksim Rakhuba, Christoph Schwab:
Tensor rank bounds for point singularities in ℝ3. Adv. Comput. Math. 48(3): 18 (2022) - [j110]Lukas Herrmann, Joost A. A. Opschoor, Christoph Schwab:
Constructive Deep ReLU Neural Network Approximation. J. Sci. Comput. 90(1): 75 (2022) - [j109]Josef Dick, Marcello Longo, Christoph Schwab:
Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification. SIAM/ASA J. Uncertain. Quantification 10(2): 651-686 (2022) - [j108]Vladimir A. Kazeev, Ivan V. Oseledets, Maxim V. Rakhuba, Christoph Schwab:
Quantized Tensor FEM for Multiscale Problems: Diffusion Problems in Two and Three Dimensions. Multiscale Model. Simul. 20(3): 893-935 (2022) - [i23]Dinh Dung, Van Kien Nguyen, Christoph Schwab, Jakob Zech:
Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs. CoRR abs/2201.01912 (2022) - [i22]Marcello Longo, Joost A. A. Opschoor, Nico Disch, Christoph Schwab, Jakob Zech:
De Rham compatible Deep Neural Networks. CoRR abs/2201.05395 (2022) - [i21]Ilaria Perugia, Christoph Schwab, Marco Zank:
Exponential Convergence of hp-Time-Stepping in Space-Time Discretizations of Parabolic PDEs. CoRR abs/2203.11879 (2022) - [i20]Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab:
Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D. CoRR abs/2204.04113 (2022) - [i19]Lukas Herrmann, Christoph Schwab, Jakob Zech:
Neural and gpc operator surrogates: construction and expression rate bounds. CoRR abs/2207.04950 (2022) - [i18]Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab:
Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons. CoRR abs/2209.11468 (2022) - [i17]Helmut Harbrecht, Michael D. Multerer, Olaf Schenk, Christoph Schwab:
Multiresolution kernel matrix algebra. CoRR abs/2211.11681 (2022) - [i16]Kristin Kirchner, Christoph Schwab:
Monte Carlo convergence rates for kth moments in Banach spaces. CoRR abs/2212.03797 (2022) - [i15]Rubén Aylwin, Carlos Jerez-Hanckes, Christoph Schwab, Jakob Zech:
Multilevel Domain Uncertainty Quantification in Computational Electromagnetics. CoRR abs/2212.07240 (2022) - 2021
- [j107]Viet Ha Hoang, Jia Hao Quek, Christoph Schwab:
Multilevel Markov Chain Monte Carlo for Bayesian Inversion of Parabolic Partial Differential Equations under Gaussian Prior. SIAM/ASA J. Uncertain. Quantification 9(2): 384-419 (2021) - [j106]Lukas Herrmann, Magdalena Keller, Christoph Schwab:
Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems. Math. Comput. 90(330): 1831-1860 (2021) - [j105]Ankit Gupta, Christoph Schwab, Mustafa Khammash:
DeepCME: A deep learning framework for computing solution statistics of the chemical master equation. PLoS Comput. Biol. 17(12) (2021) - [j104]Marcello Longo, Siddhartha Mishra, T. Konstantin Rusch, Christoph Schwab:
Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks. SIAM J. Sci. Comput. 43(6): A3938-A3966 (2021) - [i14]Lukas Gonon, Christoph Schwab:
Deep ReLU Network Expression Rates for Option Prices in high-dimensional, exponential Lévy models. CoRR abs/2101.11897 (2021) - [i13]Lukas Gonon, Christoph Schwab:
Deep ReLU Neural Network Approximation for Stochastic Differential Equations with Jumps. CoRR abs/2102.11707 (2021) - [i12]Helmut Harbrecht, Lukas Herrmann, Kristin Kirchner, Christoph Schwab:
Multilevel approximation of Gaussian random fields: Covariance compression, estimation and spatial prediction. CoRR abs/2103.04424 (2021) - [i11]Christoph Schwab, Jakob Zech:
Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in L2(Rd, γd). CoRR abs/2111.07080 (2021) - [i10]Carlo Marcati, Christoph Schwab:
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations. CoRR abs/2112.08125 (2021) - [i9]Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab:
Weighted analytic regularity for the integral fractional Laplacian in polygons. CoRR abs/2112.08151 (2021) - 2020
- [j103]Rubén Aylwin, Carlos Jerez-Hanckes, Christoph Schwab, Jakob Zech:
Domain Uncertainty Quantification in Computational Electromagnetics. SIAM/ASA J. Uncertain. Quantification 8(1): 301-341 (2020) - [j102]Michael Feischl, Christoph Schwab:
Exponential convergence in \(H^1\) of hp-FEM for Gevrey regularity with isotropic singularities. Numerische Mathematik 144(2): 323-346 (2020) - [j101]Carlo Marcati, Christoph Schwab:
Analytic Regularity for the Incompressible Navier-Stokes Equations in Polygons. SIAM J. Math. Anal. 52(3): 2945-2968 (2020) - [i8]Pratyuksh Bansal, Andrea Moiola, Ilaria Perugia, Christoph Schwab:
Space-time discontinuous Galerkin approximation of acoustic waves with point singularities. CoRR abs/2002.11575 (2020) - [i7]Lehel Banjai, Jens Markus Melenk, Christoph Schwab:
hp-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains. CoRR abs/2004.10517 (2020) - [i6]Carlo Marcati, Christoph Schwab:
Analytic regularity for the incompressible Navier-Stokes equations in polygons. CoRR abs/2004.11264 (2020) - [i5]Vladimir A. Kazeev, Ivan V. Oseledets, Maksim Rakhuba, Christoph Schwab:
Quantized tensor FEM for multiscale problems: diffusion problems in two and three dimensions. CoRR abs/2006.01455 (2020) - [i4]Marcello Longo, Siddhartha Mishra, T. Konstantin Rusch, Christoph Schwab:
Higher-order Quasi-Monte Carlo Training of Deep Neural Networks. CoRR abs/2009.02713 (2020) - [i3]Carlo Marcati, Joost A. A. Opschoor, Philipp Christian Petersen, Christoph Schwab:
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities. CoRR abs/2010.12217 (2020) - [i2]Lehel Banjai, Jens Markus Melenk, Christoph Schwab:
Exponential Convergence of hp FEM for Spectral Fractional Diffusion in Polygons. CoRR abs/2011.05701 (2020)
2010 – 2019
- 2019
- [j100]Josef Dick, Robert N. Gantner, Quoc Thong Le Gia, Christoph Schwab:
Higher order Quasi-Monte Carlo integration for Bayesian PDE Inversion. Comput. Math. Appl. 77(1): 144-172 (2019) - [j99]Lehel Banjai, Jens Markus Melenk, Ricardo H. Nochetto, Enrique Otárola, Abner J. Salgado, Christoph Schwab:
Tensor FEM for Spectral Fractional Diffusion. Found. Comput. Math. 19(4): 901-962 (2019) - [j98]Lukas Herrmann, Christoph Schwab, Jakob Zech:
Uncertainty Quantification for Spectral Fractional Diffusion: Sparsity Analysis of Parametric Solutions. SIAM/ASA J. Uncertain. Quantification 7(3): 913-947 (2019) - [j97]Lukas Herrmann, Christoph Schwab:
QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights. Numerische Mathematik 141(1): 63-102 (2019) - [j96]Josef Dick, Michael Feischl, Christoph Schwab:
Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification. SIAM J. Numer. Anal. 57(4): 1744-1769 (2019) - [i1]Carlo Marcati, Maxim V. Rakhuba, Christoph Schwab:
Tensor Rank bounds for Point Singularities in R3. CoRR abs/1912.07996 (2019) - 2018
- [j95]Ralf Hiptmair, Laura Scarabosio, Claudia Schillings, Christoph Schwab:
Large deformation shape uncertainty quantification in acoustic scattering. Adv. Comput. Math. 44(5): 1475-1518 (2018) - [j94]Dominik Schötzau, Christoph Schwab:
Exponential Convergence of hp-FEM for Elliptic Problems in Polyhedra: Mixed Boundary Conditions and Anisotropic Polynomial Degrees. Found. Comput. Math. 18(3): 595-660 (2018) - [j93]Wolfgang Dahmen, Gitta Kutyniok, Wang-Q Lim, Christoph Schwab, Gerrit Welper:
Adaptive anisotropic Petrov-Galerkin methods for first order transport equations. J. Comput. Appl. Math. 340: 191-220 (2018) - [j92]Fabian L. Mueller, Dominik Schötzau, Christoph Schwab:
Discontinuous Galerkin Methods for Acoustic Wave Propagation in Polygons. J. Sci. Comput. 77(3): 1909-1935 (2018) - [j91]Vladimir A. Kazeev, Christoph Schwab:
Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions. Numerische Mathematik 138(1): 133-190 (2018) - [j90]Albert Cohen, Christoph Schwab, Jakob Zech:
Shape Holomorphy of the Stationary Navier-Stokes Equations. SIAM J. Math. Anal. 50(2): 1720-1752 (2018) - [j89]Robert N. Gantner, Lukas Herrmann, Christoph Schwab:
Quasi-Monte Carlo Integration for Affine-Parametric, Elliptic PDEs: Local Supports and Product Weights. SIAM J. Numer. Anal. 56(1): 111-135 (2018) - 2017
- [j88]Vladimir A. Kazeev, Ivan V. Oseledets, Maksim Rakhuba, Christoph Schwab:
QTT-finite-element approximation for multiscale problems I: model problems in one dimension. Adv. Comput. Math. 43(2): 411-442 (2017) - [j87]Holger Rauhut, Christoph Schwab:
Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations. Math. Comput. 86(304): 661-700 (2017) - [j86]Frances Y. Kuo, Robert Scheichl, Christoph Schwab, Ian H. Sloan, Elisabeth Ullmann:
Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems. Math. Comput. 86(308): 2827-2860 (2017) - [j85]Jürgen Dölz, Helmut Harbrecht, Christoph Schwab:
Covariance regularity and \(\mathcal {H}\) -matrix approximation for rough random fields. Numerische Mathematik 135(4): 1045-1071 (2017) - [j84]Christoph Schwab, Rob Stevenson:
Fractional Space-Time Variational Formulations of (Navier-) Stokes Equations. SIAM J. Math. Anal. 49(4): 2442-2467 (2017) - [j83]Markus Bachmayr, Albert Cohen, Dinh Dung, Christoph Schwab:
Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs. SIAM J. Numer. Anal. 55(5): 2151-2186 (2017) - [j82]Fabian L. Müller, Dominik Schötzau, Christoph Schwab:
Symmetric Interior Penalty Discontinuous Galerkin Methods for Elliptic Problems in Polygons. SIAM J. Numer. Anal. 55(5): 2490-2521 (2017) - 2016
- [j81]Siddhartha Mishra, Christoph Schwab, Jonas Sukys:
Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium. J. Comput. Phys. 312: 192-217 (2016) - [j80]Peng Chen, Christoph Schwab:
Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations. J. Comput. Phys. 316: 470-503 (2016) - [j79]Josef Dick, Quoc Thong Le Gia, Christoph Schwab:
Higher Order Quasi-Monte Carlo Integration for Holomorphic, Parametric Operator Equations. SIAM/ASA J. Uncertain. Quantification 4(1): 48-79 (2016) - [j78]Siddhartha Mishra, Nils Henrik Risebro, Christoph Schwab, Svetlana V. Tokareva:
Numerical Solution of Scalar Conservation Laws with Random Flux Functions. SIAM/ASA J. Uncertain. Quantification 4(1): 552-591 (2016) - [j77]Angela Kunoth, Christoph Schwab:
Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems. SIAM/ASA J. Uncertain. Quantification 4(1): 1034-1059 (2016) - [j76]Dominik Schötzau, Christoph Schwab, Thomas P. Wihler:
hp-dGFEM for second-order mixed elliptic problems in polyhedra. Math. Comput. 85(299): 1051-1083 (2016) - [j75]Josef Dick, Frances Y. Kuo, Quoc Thong Le Gia, Christoph Schwab:
Multilevel Higher Order QMC Petrov-Galerkin Discretization for Affine Parametric Operator Equations. SIAM J. Numer. Anal. 54(4): 2541-2568 (2016) - 2015
- [j74]Frances Y. Kuo, Christoph Schwab, Ian H. Sloan:
Multi-level Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic PDEs with Random Coefficients. Found. Comput. Math. 15(2): 411-449 (2015) - [j73]Fabian L. Müller, Christoph Schwab:
Finite Elements with mesh refinement for wave equations in polygons. J. Comput. Appl. Math. 283: 163-181 (2015) - [j72]Stefan Pauli, Peter Arbenz, Christoph Schwab:
Intrinsic fault tolerance of multilevel Monte Carlo methods. J. Parallel Distributed Comput. 84: 24-36 (2015) - [j71]Alexey Chernov, Tobias von Petersdorff, Christoph Schwab:
Quadrature algorithms for high dimensional singular integrands on simplices. Numer. Algorithms 70(4): 847-874 (2015) - [j70]Ivan G. Graham, Frances Y. Kuo, James A. Nichols, Robert Scheichl, Christoph Schwab, Ian H. Sloan:
Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients. Numerische Mathematik 131(2): 329-368 (2015) - [j69]Claudia Schillings, Mikael Sunnåker, Jörg Stelling, Christoph Schwab:
Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks. PLoS Comput. Biol. 11(8) (2015) - [j68]Vladimir A. Kazeev, Christoph Schwab:
Tensor Approximation of Stationary Distributions of Chemical Reaction Networks. SIAM J. Matrix Anal. Appl. 36(3): 1221-1247 (2015) - [j67]Josef Dick, Frances Y. Kuo, Quoc Thong Le Gia, Christoph Schwab:
Fast QMC Matrix-Vector Multiplication. SIAM J. Sci. Comput. 37(3) (2015) - 2014
- [j66]Alexey Chernov, Christoph Schwab:
High-order finite element approximation for partial differential equations. Comput. Math. Appl. 67(4): 709-711 (2014) - [j65]Abdellah Chkifa, Albert Cohen, Christoph Schwab:
High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs. Found. Comput. Math. 14(4): 601-633 (2014) - [j64]Claude Jeffrey Gittelson, Roman Andreev, Christoph Schwab:
Optimality of adaptive Galerkin methods for random parabolic partial differential equations. J. Comput. Appl. Math. 263: 189-201 (2014) - [j63]Vladimir A. Kazeev, Mustafa Khammash, Michael Nip, Christoph Schwab:
Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains. PLoS Comput. Biol. 10(3) (2014) - [j62]Ralf Kornhuber, Christoph Schwab, Maren-Wanda Wolf:
Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities. SIAM J. Numer. Anal. 52(3): 1243-1268 (2014) - [j61]Josef Dick, Frances Y. Kuo, Quoc Thong Le Gia, Dirk Nuyens, Christoph Schwab:
Higher Order QMC Petrov-Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs. SIAM J. Numer. Anal. 52(6): 2676-2702 (2014) - [c4]Andrea Barth, Christoph Schwab, Jonas Sukys:
Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier-Stokes Equations. MCQMC 2014: 209-227 - [c3]Robert N. Gantner, Christoph Schwab:
Computational Higher Order Quasi-Monte Carlo Integration. MCQMC 2014: 271-288 - 2013
- [j60]Assyr Abdulle, Andrea Barth, Christoph Schwab:
Multilevel Monte Carlo Methods for Stochastic Elliptic Multiscale PDEs. Multiscale Model. Simul. 11(4): 1033-1070 (2013) - [j59]Alexey Chernov, Christoph Schwab:
First order k-th moment finite element analysis of nonlinear operator equations with stochastic data. Math. Comput. 82(284): 1859-1888 (2013) - [j58]Claude Jeffrey Gittelson, Juho Könnö, Christoph Schwab, Rolf Stenberg:
The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem. Numerische Mathematik 125(2): 347-386 (2013) - [j57]Angela Kunoth, Christoph Schwab:
Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs. SIAM J. Control. Optim. 51(3): 2442-2471 (2013) - [j56]Viet Ha Hoang, Christoph Schwab:
Sparse Tensor Galerkin Discretization of Parametric and Random Parabolic PDEs - Analytic Regularity and Generalized Polynomial Chaos Approximation. SIAM J. Math. Anal. 45(5): 3050-3083 (2013) - [j55]Dominik Schötzau, Christoph Schwab, Thomas P. Wihler:
hp-dGFEM for Second-Order Elliptic Problems in Polyhedra I: Stability on Geometric Meshes. SIAM J. Numer. Anal. 51(3): 1610-1633 (2013) - [j54]Dominik Schötzau, Christoph Schwab, Thomas P. Wihler:
hp-DGFEM for Second Order Elliptic Problems in Polyhedra II: Exponential Convergence. SIAM J. Numer. Anal. 51(4): 2005-2035 (2013) - [p1]Siddhartha Mishra, Christoph Schwab, Jonas Sukys:
Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws. Uncertainty Quantification in Computational Fluid Dynamics 2013: 225-294 - [e1]Hester Bijl, Didier Lucor, Siddhartha Mishra, Christoph Schwab:
Uncertainty Quantification in Computational Fluid Dynamics. Lecture Notes in Computational Science and Engineering 92, Springer 2013, ISBN 978-3-319-00884-4 [contents] - 2012
- [j53]Siddhartha Mishra, Christoph Schwab, Jonas Sukys:
Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions. J. Comput. Phys. 231(8): 3365-3388 (2012) - [j52]Siddhartha Mishra, Christoph Schwab:
Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data. Math. Comput. 81(280): 1979-2018 (2012) - [j51]Alexey Chernov, Christoph Schwab:
Exponential Convergence of Gauss-Jacobi Quadratures for Singular Integrals over Simplices in Arbitrary Dimension. SIAM J. Numer. Anal. 50(3): 1433-1455 (2012) - [j50]Wolfgang Dahmen, Chunyan Huang, Christoph Schwab, Gerrit Welper:
Adaptive Petrov-Galerkin Methods for First Order Transport Equations. SIAM J. Numer. Anal. 50(5): 2420-2445 (2012) - [j49]Frances Y. Kuo, Christoph Schwab, Ian H. Sloan:
Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients. SIAM J. Numer. Anal. 50(6): 3351-3374 (2012) - [j48]Siddhartha Mishra, Christoph Schwab, Jonas Sukys:
Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions. SIAM J. Sci. Comput. 34(6) (2012) - [c2]Markus Hansen, Claudia Schillings, Christoph Schwab:
Sparse Approximation Algorithms for High Dimensional Parametric Initial Value Problems. HPSC 2012: 63-81 - 2011
- [b1]Christoph Schwab:
Combining and extending concepts of single display groupware and tangible user interfaces for intuitive collaboration. ETH Zurich, Zürich, Switzerland, 2011 - [j47]Christoph Schwab, Claude Jeffrey Gittelson:
Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs. Acta Numer. 20: 291-467 (2011) - [j46]Konstantin Grella, Christoph Schwab:
Sparse Discrete Ordinates Method in Radiative Transfer. Comput. Methods Appl. Math. 11(3): 305-326 (2011) - [j45]Holger Brandsmeier, Kersten Schmidt, Christoph Schwab:
A multiscale hp-FEM for 2D photonic crystal bands. J. Comput. Phys. 230(2): 349-374 (2011) - [j44]Konstantin Grella, Christoph Schwab:
Sparse tensor spherical harmonics approximation in radiative transfer. J. Comput. Phys. 230(23): 8452-8473 (2011) - [j43]Andrea Barth, Christoph Schwab, Nathaniel Zollinger:
Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients. Numerische Mathematik 119(1): 123-161 (2011) - [j42]Christoph Schwab, Rob Stevenson:
Fast evaluation of nonlinear functionals of tensor product wavelet expansions. Numerische Mathematik 119(4): 765-786 (2011) - [j41]Boris N. Khoromskij, Christoph Schwab:
Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs. SIAM J. Sci. Comput. 33(1): 364-385 (2011) - [c1]Jonas Sukys, Siddhartha Mishra, Christoph Schwab:
Static Load Balancing for Multi-level Monte Carlo Finite Volume Solvers. PPAM (1) 2011: 245-254 - 2010
- [j40]Albert Cohen, Ronald A. DeVore, Christoph Schwab:
Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs. Found. Comput. Math. 10(6): 615-646 (2010) - [j39]Nils Reich, Christoph Schwab, Christoph Winter:
On Kolmogorov equations for anisotropic multivariate Lévy processes. Finance Stochastics 14(4): 527-567 (2010)
2000 – 2009
- 2009
- [j38]Norbert Hilber, Nils Reich, Christoph Schwab, Christoph Winter:
Numerical methods for Lévy processes. Finance Stochastics 13(4): 471-500 (2009) - [j37]Christoph Schwab, Rob P. Stevenson:
Space-time adaptive wavelet methods for parabolic evolution problems. Math. Comput. 78(267): 1293-1318 (2009) - [j36]Marcel Bieri, Roman Andreev, Christoph Schwab:
Sparse Tensor Discretization of Elliptic sPDEs. SIAM J. Sci. Comput. 31(6): 4281-4304 (2009) - 2008
- [j35]Gisela Widmer, Ralf Hiptmair, Christoph Schwab:
Sparse adaptive finite elements for radiative transfer. J. Comput. Phys. 227(12): 6071-6105 (2008) - [j34]Christoph Schwab, Rob P. Stevenson:
Adaptive wavelet algorithms for elliptic PDE's on product domains. Math. Comput. 77(261): 71-92 (2008) - [j33]Helmut Harbrecht, Reinhold Schneider, Christoph Schwab:
Sparse second moment analysis for elliptic problems in stochastic domains. Numerische Mathematik 109(3): 385-414 (2008) - [j32]Helmut Harbrecht, Reinhold Schneider, Christoph Schwab:
Multilevel frames for sparse tensor product spaces. Numerische Mathematik 110(2): 199 (2008) - 2006
- [j31]Christoph Schwab, Radu Alexandru Todor:
Karhunen-Loève approximation of random fields by generalized fast multipole methods. J. Comput. Phys. 217(1): 100-122 (2006) - [j30]Ana-Maria Matache, Christoph Schwab, Thomas P. Wihler:
Linear Complexity Solution of Parabolic Integro-differential Equations. Numerische Mathematik 104(1): 69-102 (2006) - [j29]Mihaela Negreanu, Ana-Maria Matache, Christoph Schwab:
Wavelet Filtering for Exact Controllability of the Wave Equation. SIAM J. Sci. Comput. 28(5): 1851-1885 (2006) - 2005
- [j28]Viet Ha Hoang, Christoph Schwab:
High-Dimensional Finite Elements for Elliptic Problems with Multiple Scales. Multiscale Model. Simul. 3(1): 168-194 (2005) - [j27]Assyr Abdulle, Christoph Schwab:
Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces. Multiscale Model. Simul. 3(1): 195-220 (2005) - [j26]Sven Beuchler, Reinhold Schneider, Christoph Schwab:
Multiresolution weighted norm equivalences and applications. Numerische Mathematik 102(2): 365-366 (2005) - [j25]Ana-Maria Matache, Christoph Schwab, Thomas P. Wihler:
Fast Numerical Solution of Parabolic Integrodifferential Equations with Applications in Finance. SIAM J. Sci. Comput. 27(2): 369-393 (2005) - 2004
- [j24]Sven Beuchler, Reinhold Schneider, Christoph Schwab:
Multiresolution weighted norm equivalences and applications. Numerische Mathematik 98(1): 67-97 (2004) - 2003
- [j23]Ana-Maria Matache, Tomás Roubícek, Christoph Schwab:
Higher-Order Convex Approximations of Young Measures in Optimal Control. Adv. Comput. Math. 19(1-3): 73-97 (2003) - [j22]Christoph Schwab, Radu Alexandru Todor:
Sparse Finite Elements for Stochastic Elliptic Problems - Higher Order Moments. Computing 71(1): 43-63 (2003) - [j21]Vít Dolejsí, Miloslav Feistauer, Christoph Schwab:
On some aspects of the discontinuous Galerkin finite element method for conservation laws. Math. Comput. Simul. 61(3-6): 333-346 (2003) - [j20]Andrea Toselli, Christoph Schwab:
Mixed HP-finite element approximations on geometric edge and boundary layer meshes in three dimensions. Numerische Mathematik 94(4): 771-801 (2003) - [j19]Annalisa Buffa, Ralf Hiptmair, Tobias von Petersdorff, Christoph Schwab:
Boundary Element Methods for Maxwell Transmission Problems in Lipschitz Domains. Numerische Mathematik 95(3): 459-485 (2003) - [j18]Christoph Schwab, Radu Alexandru Todor:
Sparse finite elements for elliptic problems with stochastic loading. Numerische Mathematik 95(4): 707-734 (2003) - [j17]Tobias von Petersdorff, Christoph Schwab:
Wavelet Discretizations of Parabolic Integrodifferential Equations. SIAM J. Numer. Anal. 41(1): 159-180 (2003) - 2002
- [j16]Paul Castillo, Bernardo Cockburn, Dominik Schötzau, Christoph Schwab:
Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems. Math. Comput. 71(238): 455-478 (2002) - [j15]Annalisa Buffa, Martin Costabel, Christoph Schwab:
Boundary element methods for Maxwell's equations on non-smooth domains. Numerische Mathematik 92(4): 679-710 (2002) - [j14]Paul Houston, Christoph Schwab, Endre Süli:
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems. SIAM J. Numer. Anal. 39(6): 2133-2163 (2002) - [j13]Ralf Hiptmair, Christoph Schwab:
Natural Boundary Element Methods for the Electric Field Integral Equation on Polyhedra. SIAM J. Numer. Anal. 40(1): 66-86 (2002) - [j12]Bernardo Cockburn, Guido Kanschat, Dominik Schötzau, Christoph Schwab:
Local Discontinuous Galerkin Methods for the Stokes System. SIAM J. Numer. Anal. 40(1): 319-343 (2002) - [j11]Dominik Schötzau, Christoph Schwab, Andrea Toselli:
Mixed hp-DGFEM for Incompressible Flows. SIAM J. Numer. Anal. 40(6): 2171-2194 (2002) - 2000
- [j10]Jens Markus Melenk, N. P. Kirchner, Christoph Schwab:
Spectral Galerkin Discretization for Hydrodynamic Stability Problems. Computing 65(2): 97-118 (2000) - [j9]Ana-Maria Matache, Ivo Babuska, Christoph Schwab:
Generalized p-FEM in homogenization. Numerische Mathematik 86(2): 319-375 (2000) - [j8]Paul Houston, Christoph Schwab, Endre Süli:
Stabilized hp-Finite Element Methods for First-Order Hyperbolic Problems. SIAM J. Numer. Anal. 37(5): 1618-1643 (2000) - [j7]Dominik Schötzau, Christoph Schwab:
Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method. SIAM J. Numer. Anal. 38(3): 837-875 (2000)
1990 – 1999
- 1999
- [j6]Christoph Schwab, Wolfgang L. Wendland:
On the extraction technique in boundary integral equations. Math. Comput. 68(225): 91-122 (1999) - [j5]Dominik Schötzau, Christoph Schwab, Rolf Stenberg:
Mixed hp-FEM on anisotropic meshes II: Hanging nodes and tensor products of boundary layer meshes. Numerische Mathematik 83(4): 667-697 (1999) - [j4]Christian Lage, Christoph Schwab:
Wavelet Galerkin Algorithms for Boundary Integral Equations. SIAM J. Sci. Comput. 20(6): 2195-2222 (1999) - 1996
- [j3]Christoph Schwab, Manil Suri:
The p and hp versions of the finite element method for problems with boundary layers. Math. Comput. 65(216): 1403-1429 (1996) - 1994
- [j2]Christoph Schwab:
Variable order composite quadrature of singular and nearly singular integrals. Computing 53(2): 173-194 (1994) - 1992
- [j1]Ralf Kieser, Christoph Schwab, Wolfgang L. Wendland:
Numerical evaluation of singular and finite-part integrals on curved surfaces using symbolic manipulation. Computing 49(3): 279-301 (1992)
Coauthor Index
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