Christoph Schwab

Publication Activity (10 Years)

Years Active: 1992-2024
Publications (10 Years): 81

Top Venues

CoRR

SIAM J. Numer. Anal.

SIAM/ASA J. Uncertain. Quantification

Numerische Mathematik

Publications

Helmut Harbrecht, Christoph Schwab, Marco Zank
Wavelet compressed, modified Hilbert transform in the space-time discretization of the heat equation. CoRR (2024)
Joost A. A. Opschoor, Christoph Schwab, Christos Xenophontos
Neural Networks for Singular Perturbations. CoRR (2024)
Marcello Longo, Christoph Schwab, Andreas Stein
A-posteriori QMC-FEM error estimation for Bayesian inversion and optimal control with entropic risk measure. CoRR (2023)
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) (2023)
Carlo Marcati, Joost A. A. Opschoor, Philipp C. Petersen, Christoph Schwab
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities. Found. Comput. Math. 23 (3) (2023)
Lehel Banjai, Jens Markus Melenk, Christoph Schwab
Exponential convergence of hp FEM for spectral fractional diffusion in polygons. Numerische Mathematik 153 (1) (2023)
Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab
Weighted analytic regularity for the integral fractional Laplacian in polyhedra. CoRR (2023)
Marcello Longo, Joost A. A. Opschoor, Nico Disch, Christoph Schwab, Jakob Zech
De Rham compatible Deep Neural Network FEM. Neural Networks 165 (2023)
Joost A. A. Opschoor, Christoph Schwab
Deep ReLU networks and high-order finite element methods II: Chebyshev emulation. CoRR (2023)
Christoph Schwab, Andreas Stein, Jakob Zech
Deep Operator Network Approximation Rates for Lipschitz Operators. CoRR (2023)
Rubén Aylwin, Fernando Henríquez, Christoph Schwab
ReLU Neural Network Galerkin BEM. J. Sci. Comput. 95 (2) (2023)
Helmut Harbrecht, Marc Schmidlin, Christoph Schwab
The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs. CoRR (2023)
Christoph Schwab, Andreas Stein
Multilevel Monte Carlo FEM for Elliptic PDEs with Besov Random Tree Priors. CoRR (2023)
Lukas Herrmann, Joost A. A. Opschoor, Christoph Schwab
Constructive Deep ReLU Neural Network Approximation. J. Sci. Comput. 90 (1) (2022)
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) (2022)
Helmut Harbrecht, Michael D. Multerer, Olaf Schenk, Christoph Schwab
Multiresolution kernel matrix algebra. CoRR (2022)
Carlo Marcati, Maksim Rakhuba, Christoph Schwab
. Adv. Comput. Math. 48 (3) (2022)
Josef Dick, Marcello Longo, Christoph Schwab
Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification. SIAM/ASA J. Uncertain. Quantification 10 (2) (2022)
Marcello Longo, Joost A. A. Opschoor, Nico Disch, Christoph Schwab, Jakob Zech
De Rham compatible Deep Neural Networks. CoRR (2022)
Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab
Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons. CoRR (2022)
Rubén Aylwin, Carlos Jerez-Hanckes, Christoph Schwab, Jakob Zech
Multilevel Domain Uncertainty Quantification in Computational Electromagnetics. CoRR (2022)
Ilaria Perugia, Christoph Schwab, Marco Zank
Exponential Convergence of hp-Time-Stepping in Space-Time Discretizations of Parabolic PDEs. CoRR (2022)
Lukas Herrmann, Christoph Schwab, Jakob Zech
Neural and gpc operator surrogates: construction and expression rate bounds. CoRR (2022)
Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab
Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D. CoRR (2022)
Kristin Kirchner, Christoph Schwab
Monte Carlo convergence rates for kth moments in Banach spaces. CoRR (2022)
Dinh Dung, Van Kien Nguyen, Christoph Schwab, Jakob Zech
Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs. CoRR (2022)
Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab
Weighted analytic regularity for the integral fractional Laplacian in polygons. CoRR (2021)
Lukas Gonon, Christoph Schwab
Deep ReLU Network Expression Rates for Option Prices in high-dimensional, exponential Lévy models. CoRR (2021)
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)
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) (2021)
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) (2021)
Carlo Marcati, Christoph Schwab
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations. CoRR (2021)
Lukas Herrmann, Magdalena Keller, Christoph Schwab
Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems. Math. Comput. 90 (330) (2021)
Lukas Gonon, Christoph Schwab
Deep ReLU Neural Network Approximation for Stochastic Differential Equations with Jumps. CoRR (2021)
Christoph Schwab, Jakob Zech
). CoRR (2021)
Helmut Harbrecht, Lukas Herrmann, Kristin Kirchner, Christoph Schwab
Multilevel approximation of Gaussian random fields: Covariance compression, estimation and spatial prediction. CoRR (2021)
Vladimir A. Kazeev, Ivan V. Oseledets, Maksim Rakhuba, Christoph Schwab
Quantized tensor FEM for multiscale problems: diffusion problems in two and three dimensions. CoRR (2020)
Rubén Aylwin, Carlos Jerez-Hanckes, Christoph Schwab, Jakob Zech
Domain Uncertainty Quantification in Computational Electromagnetics. SIAM/ASA J. Uncertain. Quantification 8 (1) (2020)
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 (2020)
Carlo Marcati, Joost A. A. Opschoor, Philipp C. Petersen, Christoph Schwab
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities. CoRR (2020)
Michael Feischl, Christoph Schwab
-FEM for Gevrey regularity with isotropic singularities. Numerische Mathematik 144 (2) (2020)
Carlo Marcati, Christoph Schwab
Analytic regularity for the incompressible Navier-Stokes equations in polygons. CoRR (2020)
Marcello Longo, Siddhartha Mishra, T. Konstantin Rusch, Christoph Schwab
Higher-order Quasi-Monte Carlo Training of Deep Neural Networks. CoRR (2020)
Pratyuksh Bansal, Andrea Moiola, Ilaria Perugia, Christoph Schwab
Space-time discontinuous Galerkin approximation of acoustic waves with point singularities. CoRR (2020)
Lehel Banjai, Jens Markus Melenk, Christoph Schwab
Exponential Convergence of hp FEM for Spectral Fractional Diffusion in Polygons. CoRR (2020)
Carlo Marcati, Christoph Schwab
Analytic Regularity for the Incompressible Navier-Stokes Equations in Polygons. SIAM J. Math. Anal. 52 (3) (2020)
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) (2019)
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) (2019)
Carlo Marcati, Maxim V. Rakhuba, Christoph Schwab
. CoRR (2019)
Lukas Herrmann, Christoph Schwab
QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights. Numerische Mathematik 141 (1) (2019)
Josef Dick, Michael Feischl, Christoph Schwab
Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification. SIAM J. Numer. Anal. 57 (4) (2019)
Lukas Herrmann, Christoph Schwab, Jakob Zech
Uncertainty Quantification for Spectral Fractional Diffusion: Sparsity Analysis of Parametric Solutions. SIAM/ASA J. Uncertain. Quantification 7 (3) (2019)
Fabian L. Mueller, Dominik Schötzau, Christoph Schwab
Discontinuous Galerkin Methods for Acoustic Wave Propagation in Polygons. J. Sci. Comput. 77 (3) (2018)
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) (2018)
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 (2018)
Vladimir A. Kazeev, Christoph Schwab
Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions. Numerische Mathematik 138 (1) (2018)
Ralf Hiptmair, Laura Scarabosio, Claudia Schillings, Christoph Schwab
Large deformation shape uncertainty quantification in acoustic scattering. Adv. Comput. Math. 44 (5) (2018)
Albert Cohen, Christoph Schwab, Jakob Zech
Shape Holomorphy of the Stationary Navier-Stokes Equations. SIAM J. Math. Anal. 50 (2) (2018)
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) (2018)
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) (2017)
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) (2017)
Markus Bachmayr, Albert Cohen, Dinh Dung, Christoph Schwab
Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs. SIAM J. Numer. Anal. 55 (5) (2017)
Fabian L. Müller, Dominik Schötzau, Christoph Schwab
Symmetric Interior Penalty Discontinuous Galerkin Methods for Elliptic Problems in Polygons. SIAM J. Numer. Anal. 55 (5) (2017)
Jürgen Dölz, Helmut Harbrecht, Christoph Schwab
Covariance regularity and \(\mathcal {H}\) -matrix approximation for rough random fields. Numerische Mathematik 135 (4) (2017)
Holger Rauhut, Christoph Schwab
Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations. Math. Comput. 86 (304) (2017)
Christoph Schwab, Rob Stevenson
Fractional Space-Time Variational Formulations of (Navier-) Stokes Equations. SIAM J. Math. Anal. 49 (4) (2017)
Angela Kunoth, Christoph Schwab
Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems. SIAM/ASA J. Uncertain. Quantification 4 (1) (2016)
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) (2016)
Peng Chen, Christoph Schwab
Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations. J. Comput. Phys. 316 (2016)
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 (2016)
Dominik Schötzau, Christoph Schwab, Thomas P. Wihler
hp-dGFEM for second-order mixed elliptic problems in polyhedra. Math. Comput. 85 (299) (2016)
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) (2016)
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) (2016)
Alexey Chernov, Tobias von Petersdorff, Christoph Schwab
Quadrature algorithms for high dimensional singular integrands on simplices. Numer. Algorithms 70 (4) (2015)
Stefan Pauli, Peter Arbenz, Christoph Schwab
Intrinsic fault tolerance of multilevel Monte Carlo methods. J. Parallel Distributed Comput. 84 (2015)
Fabian L. Müller, Christoph Schwab
Finite Elements with mesh refinement for wave equations in polygons. J. Comput. Appl. Math. 283 (2015)
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) (2015)
Josef Dick, Frances Y. Kuo, Quoc Thong Le Gia, Christoph Schwab
Fast QMC Matrix-Vector Multiplication. SIAM J. Sci. Comput. 37 (3) (2015)
Claudia Schillings, Mikael Sunnåker, Jörg Stelling, Christoph Schwab
Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks. PLoS Comput. Biol. 11 (8) (2015)
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) (2015)
Vladimir A. Kazeev, Christoph Schwab
Tensor Approximation of Stationary Distributions of Chemical Reaction Networks. SIAM J. Matrix Anal. Appl. 36 (3) (2015)
Andrea Barth, Christoph Schwab, Jonas Sukys
Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier-Stokes Equations. MCQMC (2014)
Abdellah Chkifa, Albert Cohen, Christoph Schwab
High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs. Found. Comput. Math. 14 (4) (2014)
Claude Jeffrey Gittelson, Roman Andreev, Christoph Schwab
Optimality of adaptive Galerkin methods for random parabolic partial differential equations. J. Comput. Appl. Math. 263 (2014)
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) (2014)
Robert N. Gantner, Christoph Schwab
Computational Higher Order Quasi-Monte Carlo Integration. MCQMC (2014)
Alexey Chernov, Christoph Schwab
High-order finite element approximation for partial differential equations. Comput. Math. Appl. 67 (4) (2014)
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)
Ralf Kornhuber, Christoph Schwab, Maren-Wanda Wolf
Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities. SIAM J. Numer. Anal. 52 (3) (2014)
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) (2013)
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) (2013)
Assyr Abdulle, Andrea Barth, Christoph Schwab
Multilevel Monte Carlo Methods for Stochastic Elliptic Multiscale PDEs. Multiscale Model. Simul. 11 (4) (2013)
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) (2013)
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) (2013)
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) (2013)
Alexey Chernov, Christoph Schwab
First order k-th moment finite element analysis of nonlinear operator equations with stochastic data. Math. Comput. 82 (284) (2013)
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)
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) (2012)
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) (2012)
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) (2012)

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Publication Activity (10 Years)

Top Topics

Top Venues

Christoph Schwab