Christoph Schwab
Orcid: 0000-0002-7570-1472Affiliations:
- ETH Zurich, Switzerland
According to our database1,
Christoph Schwab
authored at least 154 papers
between 1992 and 2024.
Collaborative distances:
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on zbmath.org
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on d-nb.info
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Bibliography
2024
Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction.
Adv. Comput. Math., October, 2024
Neural and spectral operator surrogates: unified construction and expression rate bounds.
Adv. Comput. Math., August, 2024
Analytic Regularity of Solutions to the Navier-Stokes Equations with Mixed Boundary Conditions in Polygons.
SIAM J. Math. Anal., 2024
Frequency-Explicit Shape Holomorphy in Uncertainty Quantification for Acoustic Scattering.
CoRR, 2024
Exponential Convergence of <i>hp</i>-ILGFEM for semilinear elliptic boundary value problems with monomial reaction.
CoRR, 2024
Exponential Expressivity of ReLU<sup>k</sup> Neural Networks on Gevrey Classes with Point Singularities.
CoRR, 2024
Wavelet compressed, modified Hilbert transform in the space-time discretization of the heat equation.
CoRR, 2024
Comput. Math. Appl., 2024
2023
Exponential Convergence of \(hp\)-FEM for the Integral Fractional Laplacian in Polygons.
SIAM J. Numer. Anal., December, 2023
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations.
SIAM J. Numer. Anal., June, 2023
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities.
Found. Comput. Math., June, 2023
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, March, 2023
Numerische Mathematik, 2023
CoRR, 2023
The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs.
CoRR, 2023
CoRR, 2023
CoRR, 2023
A-posteriori QMC-FEM error estimation for Bayesian inversion and optimal control with entropic risk measure.
CoRR, 2023
2022
Quantized Tensor FEM for Multiscale Problems: Diffusion Problems in Two and Three Dimensions.
Multiscale Model. Simul., September, 2022
Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification.
SIAM/ASA J. Uncertain. Quantification, 2022
CoRR, 2022
CoRR, 2022
CoRR, 2022
Exponential Convergence of hp-Time-Stepping in Space-Time Discretizations of Parabolic PDEs.
CoRR, 2022
Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs.
CoRR, 2022
Adv. Comput. Math., 2022
2021
SIAM J. Sci. Comput., 2021
DeepCME: A deep learning framework for computing solution statistics of the chemical master equation.
PLoS Comput. Biol., 2021
Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems.
Math. Comput., 2021
Multilevel Markov Chain Monte Carlo for Bayesian Inversion of Parabolic Partial Differential Equations under Gaussian Prior.
SIAM/ASA J. Uncertain. Quantification, 2021
CoRR, 2021
Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in L<sup>2</sup>(R<sup>d</sup>, γ<sub>d</sub>).
CoRR, 2021
Deep ReLU Neural Network Approximation for Stochastic Differential Equations with Jumps.
CoRR, 2021
Deep ReLU Network Expression Rates for Option Prices in high-dimensional, exponential Lévy models.
CoRR, 2021
2020
SIAM J. Math. Anal., 2020
Exponential convergence in \(H^1\) of <i>hp</i>-FEM for Gevrey regularity with isotropic singularities.
Numerische Mathematik, 2020
SIAM/ASA J. Uncertain. Quantification, 2020
hp-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains.
CoRR, 2020
Space-time discontinuous Galerkin approximation of acoustic waves with point singularities.
CoRR, 2020
2019
Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification.
SIAM J. Numer. Anal., 2019
QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights.
Numerische Mathematik, 2019
Uncertainty Quantification for Spectral Fractional Diffusion: Sparsity Analysis of Parametric Solutions.
SIAM/ASA J. Uncertain. Quantification, 2019
Comput. Math. Appl., 2019
2018
Quasi-Monte Carlo Integration for Affine-Parametric, Elliptic PDEs: Local Supports and Product Weights.
SIAM J. Numer. Anal., 2018
SIAM J. Math. Anal., 2018
Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions.
Numerische Mathematik, 2018
J. Sci. Comput., 2018
J. Comput. Appl. Math., 2018
Exponential Convergence of hp-FEM for Elliptic Problems in Polyhedra: Mixed Boundary Conditions and Anisotropic Polynomial Degrees.
Found. Comput. Math., 2018
Adv. Comput. Math., 2018
2017
Symmetric Interior Penalty Discontinuous Galerkin Methods for Elliptic Problems in Polygons.
SIAM J. Numer. Anal., 2017
SIAM J. Numer. Anal., 2017
SIAM J. Math. Anal., 2017
Covariance regularity and \(\mathcal {H}\) -matrix approximation for rough random fields.
Numerische Mathematik, 2017
Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations.
Math. Comput., 2017
Math. Comput., 2017
QTT-finite-element approximation for multiscale problems I: model problems in one dimension.
Adv. Comput. Math., 2017
2016
Multilevel Higher Order QMC Petrov-Galerkin Discretization for Affine Parametric Operator Equations.
SIAM J. Numer. Anal., 2016
SIAM/ASA J. Uncertain. Quantification, 2016
Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems.
SIAM/ASA J. Uncertain. Quantification, 2016
Higher Order Quasi-Monte Carlo Integration for Holomorphic, Parametric Operator Equations.
SIAM/ASA J. Uncertain. Quantification, 2016
Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium.
J. Comput. Phys., 2016
Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations.
J. Comput. Phys., 2016
2015
SIAM J. Matrix Anal. Appl., 2015
Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks.
PLoS Comput. Biol., 2015
Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients.
Numerische Mathematik, 2015
Numer. Algorithms, 2015
J. Parallel Distributed Comput., 2015
J. Comput. Appl. Math., 2015
Multi-level Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic PDEs with Random Coefficients.
Found. Comput. Math., 2015
2014
Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities.
SIAM J. Numer. Anal., 2014
Higher Order QMC Petrov-Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs.
SIAM J. Numer. Anal., 2014
PLoS Comput. Biol., 2014
Optimality of adaptive Galerkin methods for random parabolic partial differential equations.
J. Comput. Appl. Math., 2014
High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs.
Found. Comput. Math., 2014
Comput. Math. Appl., 2014
Proceedings of the Monte Carlo and Quasi-Monte Carlo Methods, 2014
Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier-Stokes Equations.
Proceedings of the Monte Carlo and Quasi-Monte Carlo Methods, 2014
2013
Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws.
Proceedings of the Uncertainty Quantification in Computational Fluid Dynamics, 2013
hp-DGFEM for Second Order Elliptic Problems in Polyhedra II: Exponential Convergence.
SIAM J. Numer. Anal., 2013
hp-dGFEM for Second-Order Elliptic Problems in Polyhedra I: Stability on Geometric Meshes.
SIAM J. Numer. Anal., 2013
Sparse Tensor Galerkin Discretization of Parametric and Random Parabolic PDEs - Analytic Regularity and Generalized Polynomial Chaos Approximation.
SIAM J. Math. Anal., 2013
Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs.
SIAM J. Control. Optim., 2013
Numerische Mathematik, 2013
First order k-th moment finite element analysis of nonlinear operator equations with stochastic data.
Math. Comput., 2013
Multiscale Model. Simul., 2013
2012
Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions.
SIAM J. Sci. Comput., 2012
Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients.
SIAM J. Numer. Anal., 2012
SIAM J. Numer. Anal., 2012
Exponential Convergence of Gauss-Jacobi Quadratures for Singular Integrals over Simplices in Arbitrary Dimension.
SIAM J. Numer. Anal., 2012
Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data.
Math. Comput., 2012
Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions.
J. Comput. Phys., 2012
Sparse Approximation Algorithms for High Dimensional Parametric Initial Value Problems.
Proceedings of the Modeling, Simulation and Optimization of Complex Processes, 2012
2011
Combining and extending concepts of single display groupware and tangible user interfaces for intuitive collaboration.
PhD thesis, 2011
SIAM J. Sci. Comput., 2011
Numerische Mathematik, 2011
Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients.
Numerische Mathematik, 2011
J. Comput. Phys., 2011
Comput. Methods Appl. Math., 2011
Acta Numer., 2011
Proceedings of the Parallel Processing and Applied Mathematics, 2011
2010
Finance Stochastics, 2010
Convergence Rates of Best <i>N</i>-term Galerkin Approximations for a Class of Elliptic sPDEs.
Found. Comput. Math., 2010
2009
Math. Comput., 2009
2008
Numerische Mathematik, 2008
Math. Comput., 2008
2006
SIAM J. Sci. Comput., 2006
Numerische Mathematik, 2006
J. Comput. Phys., 2006
2005
Fast Numerical Solution of Parabolic Integrodifferential Equations with Applications in Finance.
SIAM J. Sci. Comput., 2005
Multiscale Model. Simul., 2005
Multiscale Model. Simul., 2005
2004
Numerische Mathematik, 2004
2003
SIAM J. Numer. Anal., 2003
Mixed <i>HP</i>-finite element approximations on geometric edge and boundary layer meshes in three dimensions.
Numerische Mathematik, 2003
Numerische Mathematik, 2003
Numerische Mathematik, 2003
On some aspects of the discontinuous Galerkin finite element method for conservation laws.
Math. Comput. Simul., 2003
Computing, 2003
Adv. Comput. Math., 2003
2002
Discontinuous <i>hp</i>-Finite Element Methods for Advection-Diffusion-Reaction Problems.
SIAM J. Numer. Anal., 2002
Natural Boundary Element Methods for the Electric Field Integral Equation on Polyhedra.
SIAM J. Numer. Anal., 2002
SIAM J. Numer. Anal., 2002
Numerische Mathematik, 2002
Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems.
Math. Comput., 2002
2000
Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method.
SIAM J. Numer. Anal., 2000
SIAM J. Numer. Anal., 2000
Computing, 2000
1999
SIAM J. Sci. Comput., 1999
Mixed hp-FEM on anisotropic meshes II: Hanging nodes and tensor products of boundary layer meshes.
Numerische Mathematik, 1999
1996
The p and hp versions of the finite element method for problems with boundary layers.
Math. Comput., 1996
1994
Computing, 1994
1992
Numerical evaluation of singular and finite-part integrals on curved surfaces using symbolic manipulation.
Computing, 1992