Christoph Schwab
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German mathematician
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Mathematics
Christoph Schwab's Degrees
- PhD Mathematics University of Tübingen
Why Is Christoph Schwab Influential?
(Suggest an Edit or Addition)According to Wikipedia, Christoph Schwab is a German applied mathematician, specializing in numerical analysis of partial differential equations and boundary integral equations. Education and career He studied mathematics from 1982 to 1985 at the Technische Universität Darmstadt. By means of a Fulbright Scholarship, from 1985 he studied at the University of Maryland, College Park, where he received his PhD in 1989. His thesis Dimensional Reduction for Elliptic Boundary Value Problems was written under the supervision of Ivo Babuška. Schwab was a postdoc for the academic year 1989–1990 at London's University of Westminster. At the University of Maryland, Baltimore County he was an assistant professor from 1990 to 1995 and was appointed in 1995 an associate professor. At ETH Zurich, Schwab was from 1995 to 1998 an associate professor and is since 1998 a full professor. For the academic year 1993–1994 he was a visiting scientist at the IBM Deutschland Wissenschaftliches Zentrum in Heidelberg.
Christoph Schwab's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- P- and hp- finite element methods : theory and applications in solid and fluid mechanics (1998) (846)
- Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems (2001) (520)
- Boundary Element Methods (2010) (455)
- Finite elements for elliptic problems with stochastic coefficients (2005) (397)
- Karhunen-Loève approximation of random fields by generalized fast multipole methods (2006) (381)
- Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs (2010) (341)
- Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients (2011) (333)
- Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs* (2011) (279)
- Local Discontinuous Galerkin Methods for the Stokes System (2002) (269)
- ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S (2011) (257)
- Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients (2007) (240)
- Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problems (2002) (238)
- Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients (2012) (227)
- Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method (2000) (216)
- Space-time adaptive wavelet methods for parabolic evolution problems (2009) (200)
- The p and hp versions of the finite element method for problems with boundary layers (1996) (194)
- High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs (2014) (192)
- Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs (2011) (192)
- Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDEs (2010) (186)
- Fast deterministic pricing of options on Lévy driven assets (2002) (177)
- Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs (2015) (173)
- Mixed hp-DGFEM for Incompressible Flows (2002) (171)
- Sparse finite elements for elliptic problems with stochastic loading (2003) (170)
- On numerical cubatures of singular surface integrals in boundary element methods (1992) (163)
- Stabilized hp-Finite Element Methods for First-Order Hyperbolic Problems (2000) (161)
- Adaptive Petrov-Galerkin Methods for First Order Transport Equations (2011) (160)
- Sparse high order FEM for elliptic sPDEs (2009) (154)
- Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains (2014) (153)
- NUMERICAL SOLUTION OF PARABOLIC EQUATIONS IN HIGH DIMENSIONS (2004) (151)
- Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ (2018) (148)
- Isotropic Gaussian random fields on the sphere: Regularity, fast simulation and stochastic partial differential equations (2013) (146)
- Wavelet Galerkin pricing of American options on Lévy driven assets (2005) (144)
- Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data (2012) (143)
- Sparse second moment analysis for elliptic problems in stochastic domains (2008) (130)
- Boundary Element Methods for Maxwell Transmission Problems in Lipschitz Domains (2003) (127)
- Boundary element methods for Maxwell's equations on non-smooth domains (2002) (125)
- Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions (2012) (124)
- An hp a priori error analysis of¶the DG time-stepping method for initial value problems (2000) (123)
- Sparse, adaptive Smolyak quadratures for Bayesian inverse problems (2013) (123)
- Sparse Tensor Discretization of Elliptic sPDEs (2009) (119)
- Wavelet approximations for first kind boundary integral equations on polygons (1996) (117)
- Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients (2015) (116)
- Multiwavelets for Second-Kind Integral Equations (1997) (115)
- High-Dimensional Finite Elements for Elliptic Problems with Multiple Scales (2003) (115)
- Adaptive stochastic Galerkin FEM (2014) (115)
- Fully discrete hp-finite elements: fast quadrature (2001) (114)
- A-posteriori modeling error estimation for hierarchic plate models (1996) (113)
- Sparse deterministic approximation of Bayesian inverse problems (2011) (112)
- Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs (2011) (108)
- Fast Numerical Solution of Parabolic Integrodifferential Equations with Applications in Finance (2005) (108)
- Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces (2005) (105)
- hp-discontinuous Galerkin time stepping for parabolic problems (2001) (104)
- Existence of global weak solutions for some polymeric flow models (2005) (99)
- Wavelet Galerkin Algorithms for Boundary Integral Equations (1999) (99)
- Complexity analysis of accelerated MCMC methods for Bayesian inversion (2012) (98)
- Deep ReLU networks and high-order finite element methods (2020) (95)
- EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS (2005) (93)
- Discontinuous hp-finite element methods for advection-diffusion problems (2000) (93)
- Generalized p-FEM in homogenization (2000) (92)
- Multi-level Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic PDEs with Random Coefficients (2015) (92)
- Hierarchic models for laminated plates and shells (1999) (91)
- Kernel Properties and Representations of Boundary Integral Operators (1992) (91)
- Finite element analysis of nonlinear orthotropic hyperelastic membranes (1996) (90)
- Sparse Finite Elements for Stochastic Elliptic Problems – Higher Order Moments (2003) (86)
- Higher Order QMC Petrov-Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs (2014) (86)
- On some aspects of the discontinuous Galerkin finite element method for conservation laws (2003) (85)
- DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing (2018) (84)
- Variable order composite quadrature of singular and nearly singular integrals (1994) (83)
- Fully Discrete Multiscale Galerkin BEM (1997) (83)
- Multilevel Monte Carlo method for parabolic stochastic partial differential equations (2013) (79)
- Locking effects in the finite element approximation of plate models (1995) (78)
- Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems (2015) (76)
- Two-scale FEM for homogenization problems (2002) (75)
- Sparse tensor spherical harmonics approximation in radiative transfer (2011) (72)
- Fourier mode analysis of layers in shallow shell deformations (2001) (71)
- Sparse finite element methods for operator equations with stochastic data (2006) (70)
- The hp finite element method for problems in mechanics with boundary layers (1998) (70)
- An Adaptive Wavelet Method for Solving High-Dimensional Elliptic PDEs (2009) (69)
- Computational Methods for Quantitative Finance: Finite Element Methods for Derivative Pricing (2013) (68)
- Elliptic Differential Equations (2010) (68)
- QUASI-MONTE CARLO METHODS FOR HIGH-DIMENSIONAL INTEGRATION: THE STANDARD (WEIGHTED HILBERT SPACE) SETTING AND BEYOND (2011) (68)
- Uncertainty Quantification in Computational Fluid Dynamics (2013) (66)
- A posteriori error estimation for hierarchic models of elliptic boundary value problems on thin domains (1996) (66)
- Natural Boundary Element Methods for the Electric Field Integral Equation on Polyhedra (2002) (65)
- A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes (2013) (64)
- hp FEM for Reaction-Diffusion Equations I: Robust Exponential Convergence (1998) (61)
- Identification of response functions from axisymmetric membrane inflation tests: Implications for biomechanics (1994) (60)
- Quadrature for hp-Galerkin BEM in lR3 (1997) (58)
- hp-finite element methods for hyperbolic problems (1999) (58)
- Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs (2013) (57)
- hp-DGFEM for Second Order Elliptic Problems in Polyhedra II: Exponential Convergence (2013) (55)
- HP90: A general and flexible Fortran 90 hp-FE code (1998) (55)
- Sparse adaptive finite elements for radiative transfer (2008) (55)
- Large deformation shape uncertainty quantification in acoustic scattering (2018) (54)
- Multilevel frames for sparse tensor product spaces (2008) (54)
- Mixed hp-FEM on anisotropic meshes II: Hanging nodes and tensor products of boundary layer meshes (1999) (54)
- A finite volume discontinuous Galerkin scheme¶for nonlinear convection–diffusion problems (2002) (54)
- Exponential convergence of the hp-DGFEM for diffusion problems (2003) (52)
- Analytic regularity of Stokes flow on polygonal domains in countably weighted Sobolev spaces (2006) (52)
- On the extraction technique in boundary integral equations (1999) (52)
- Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations (2014) (52)
- Sparsity in Bayesian inversion of parametric operator equations (2014) (50)
- N-term Wiener chaos approximation rates for elliptic PDEs with lognormal Gaussian random inputs (2014) (50)
- Sparse Wavelet Methods for Option Pricing under Stochastic Volatility (2005) (49)
- Higher Order Quasi-Monte Carlo Integration for Holomorphic, Parametric Operator Equations (2014) (49)
- Multiresolution weighted norm equivalences and applications (2004) (49)
- Adaptive wavelet algorithms for elliptic PDE's on product domains (2008) (48)
- Numerical methods for Lévy processes (2009) (48)
- Tensor FEM for Spectral Fractional Diffusion (2017) (47)
- Numerical Solution of Scalar Conservation Laws with Random Flux Functions (2016) (46)
- Mixed hp - FEM on anisotropic meshes (1998) (45)
- Sparse finite element approximation of high-dimensional transport-dominated diffusion problems (2008) (44)
- On Kolmogorov equations for anisotropic multivariate Lévy processes (2010) (44)
- First order k-th moment finite element analysis of nonlinear operator equations with stochastic data (2013) (43)
- On singularities of solutions to the Dirichlet problem of hydrodynamics near the vertex of a cone. (1994) (43)
- Scaling limits in computational Bayesian inversion (2014) (43)
- Lévy Matters I (2010) (42)
- ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF STOCHASTIC, PARAMETRIC ELLIPTIC MULTISCALE PDEs (2013) (42)
- Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions (2012) (42)
- Maxwell eigenvalues and discrete compactness in two dimensions (2000) (42)
- Low-rank tensor structure of linear diffusion operators in the TT and QTT formats☆ (2013) (42)
- Multilevel Higher Order QMC Petrov-Galerkin Discretization for Affine Parametric Operator Equations (2016) (42)
- Sparse-grid, reduced-basis Bayesian inversion (2015) (41)
- Exponential convergence of hp quadrature for integral operators with Gevrey kernels (2011) (41)
- hp-dGFEM for Second-Order Elliptic Problems in Polyhedra I: Stability on Geometric Meshes (2013) (39)
- Sparse tensor approximation of parametric eigenvalue problems (2012) (37)
- Generalized FEM for Homogenization Problems (2002) (37)
- Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions (2018) (37)
- Multilevel higher-order quasi-Monte Carlo Bayesian estimation (2016) (36)
- Electromagnetic wave scattering by random surfaces: Shape holomorphy (2017) (36)
- Approximation on Simplices with Respect to Weighted Sobolev Norms (2000) (36)
- Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws (2013) (35)
- Boundary layers of hierarchical beam and plate models (1995) (35)
- The optimal p -version approximation of singularities on polyhedra in the boundary element method (1996) (35)
- Computational Higher Order Quasi-Monte Carlo Integration (2014) (35)
- Quadrature for $hp$-Galerkin BEM in ${\hbox{\sf l\kern-.13em R}}^3$ (1997) (35)
- Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations (2016) (34)
- Hp-DGFEM for Partial Di erential Equations with Nonegative Characteristic Form (1999) (34)
- Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium (2014) (34)
- Analytic regularity and nonlinear approximation of a class of parametric semilinear elliptic PDEs (2013) (33)
- Multilevel Monte Carlo Methods for Stochastic Elliptic Multiscale PDEs (2013) (33)
- Sparse Adaptive Approximation of High Dimensional Parametric Initial Value Problems (2013) (33)
- Multi-level Monte Carlo finite element method for elliptic PDE's with stochastic coefficients (2010) (33)
- On the posteriori estimation of the modeling error for the heat conduction in a plate and its use for adaptive hierarchical modeling (1994) (33)
- Homogenization via p -FEM for problems with microstructure (2000) (33)
- Rapid solution of first kind boundary integral equations in R3 (2003) (32)
- Anisotropic Stable Levy Copula Processes - Analytical and Numerical Aspects (2007) (32)
- Fast numerical solution of the linearized Molodensky problem (2001) (32)
- Higher order QMC Galerkin discretization for parametric operator equations (2013) (32)
- Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs (2017) (32)
- HIGH-ORDER GALERKIN APPROXIMATIONS FOR PARAMETRIC SECOND-ORDER ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS (2013) (32)
- Wavelet Discretizations of Parabolic Integrodifferential Equations (2003) (31)
- Shape Holomorphy of the Stationary Navier-Stokes Equations (2018) (29)
- Static Load Balancing for Multi-level Monte Carlo Finite Volume Solvers (2011) (29)
- Preconditioning of the second‐kind boundary integral equations for 3D eddy current problems (2001) (29)
- Sparse Tensor Galerkin Discretization of Parametric and Random Parabolic PDEs - Analytic Regularity and Generalized Polynomial Chaos Approximation (2013) (29)
- Convergence rates of high dimensional Smolyak quadrature (2020) (29)
- Tensor Approximation of Stationary Distributions of Chemical Reaction Networks (2015) (29)
- An hp finite element method for convection-diffusion problems in one dimension (1999) (28)
- Higher order Quasi-Monte Carlo integration for Bayesian Estimation (2016) (28)
- Mixed hp finite element methods for Stokes and non-Newtonian flow (1999) (27)
- The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem (2013) (27)
- QMC Galerkin Discretization of Parametric Operator Equations (2013) (27)
- QTT-finite-element approximation for multiscale problems I: model problems in one dimension (2017) (27)
- Analytic regularity for a singularly perturbed problem (1999) (27)
- Quasi-Monte Carlo Integration for Affine-Parametric, Elliptic PDEs: Local Supports and Product Weights (2018) (26)
- REGULARITY AND GENERALIZED POLYNOMIAL CHAOS APPROXIMATION OF PARAMETRIC AND RANDOM SECOND-ORDER HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS (2012) (26)
- Linear Complexity Solution of Parabolic Integro-differential Equations (2006) (26)
- Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-DGFEM (2012) (25)
- A general high‐order finite element formulation for shells at large strains and finite rotations (2003) (25)
- On singularities of solutions of the displacement problem of linear elasticity near the vertex of a cone (1992) (25)
- Finite Elements with mesh refinement for wave equations in polygons (2013) (25)
- Sparse tensor Galerkin discretizations for parametric and random parabolic PDEs I: Analytic regularity and gpc-approximation ! (2010) (25)
- The computation of potentials near and on the boundary by an extraction technique for boundary element methods (1998) (25)
- Multilevel approximation of parametric and stochastic PDES (2019) (25)
- High order approximation of probabilistic shock profiles in hyperbolic conservation laws with uncertain initial data (2013) (25)
- Coupling of an Interior Navier—Stokes Problem with an Exterior Oseen Problem (2001) (24)
- Analysis of membrane locking in hp FEM for a cylindrical shell (1998) (24)
- Deep neural network expression of posterior expectations in Bayesian PDE inversion (2020) (24)
- Adaptive Sparse Grid Model Order Reduction for Fast Bayesian Estimation and Inversion (2016) (24)
- Covariance regularity and H-matrix approximation for rough random fields (2014) (23)
- Multi-level higher order QMC Galerkin discretization for affine parametric operator equations (2014) (22)
- hp-dGFEM for second-order mixed elliptic problems in polyhedra (2015) (22)
- Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models (2021) (22)
- Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks (2015) (22)
- Multi-level Monte Carlo finite volume methods for shallow water equations with uncertain topography in multi-dimensions (2011) (22)
- Stabilized hp-DGFEM for Incompressible Flow (2003) (22)
- Mixed hp-DGFEM for incompressible flows. II: Geometric edge meshes (2004) (22)
- Boundary element methods for Maxwell equations in Lipschitz domains (2001) (22)
- Multilevel approximation of Gaussian random fields: Fast simulation (2019) (22)
- THE METHOD OF ARBITRARY LINES (1991) (22)
- Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems (2016) (21)
- Multilevel quasi-Monte Carlo integration with product weights for elliptic PDEs with lognormal coefficients (2019) (21)
- Mixed HP-finite element approximations on geometric edge and boundary layer meshes in three dimensions (2003) (21)
- A multilevel Monte Carlo finite difference method for random scalar degenerate convection–diffusion equations (2017) (21)
- Multi-level Compressed Sensing Petrov-Galerkin discretization of high-dimensional parametric PDEs (2017) (21)
- Wavelet solution of variable order pseudodifferential equations (2010) (20)
- Exponential convergence for hp-version and spectral finite element methods for elliptic problems in polyhedra (2015) (20)
- CORRECTION TO “QUASI-MONTE CARLO METHODS FOR HIGH-DIMENSIONAL INTEGRATION: THE STANDARD (WEIGHTED HILBERT SPACE) SETTING AND BEYOND” (2012) (20)
- Fractional Space-Time Variational Formulations of (Navier-) Stokes Equations (2017) (20)
- Higher order Quasi-Monte Carlo integration for Bayesian PDE Inversion (2019) (19)
- Space-time variational saddle point formulations of Stokes and Navier-Stokes equations (2014) (19)
- QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights (2018) (19)
- On the Justification of Plate Models (2011) (19)
- ON COUPLED PROBLEMS FOR VISCOUS FLOW IN EXTERIOR DOMAINS (1998) (19)
- Intrinsic fault tolerance of multilevel Monte Carlo methods (2015) (19)
- Covariance regularity and $$\mathcal {H}$$H-matrix approximation for rough random fields (2017) (18)
- Space–time hp-approximation of parabolic equations (2018) (18)
- Exponential convergence in a Galerkin least squares hp‐FEM for Stokes flow (2001) (18)
- hp-FEM for Fluid Flow Simulation (1999) (18)
- Multiresolution weighted norm equivalences and applications (2005) (17)
- Numerical evaluation of singular and finite-part integrals on curved surfaces using symbolic manipulation (1992) (17)
- Exponential Convergence of the hp Version of Isogeometric Analysis in 1D (2012) (17)
- Model order reduction methods in computational uncertainty quantification (2017) (17)
- hp FEM for reaction-diffusion equations (1997) (17)
- High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs (2013) (16)
- On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow (2002) (16)
- Sparse p-version BEM for first kind boundary integral equations with random loading (2009) (16)
- Numerical analysis of lognormal diffusions on the sphere (2016) (16)
- Higher-Order Convex Approximations of Young Measures in Optimal Control (2003) (16)
- An hp finite element method for convection-diffusion problems (1997) (16)
- Optimality of adaptive Galerkin methods for random parabolic partial differential equations (2014) (15)
- Spectral Galerkin Discretization for Hydrodynamic Stability Problems (2000) (15)
- hp-DG-QTT solution of high-dimensional degenerate diffusion equations (2012) (15)
- Sparse MCMC gpc finite element methods for Bayesian inverse problems (2012) (15)
- Sparse Discrete Ordinates Method in Radiative Transfer (2011) (15)
- Multilevel Monte Carlo front-tracking for random scalar conservation laws (2016) (14)
- Space-time discontinuous Galerkin approximation of acoustic waves with point singularities (2020) (14)
- Optimal Shear Correction Factors in Hierarchical Plte Modelling (1991) (14)
- Deep ReLU Neural Network Expression Rates for Data-to-QoI Maps in Bayesian PDE Inversion (2020) (14)
- Wavelet Filtering for Exact Controllability of the Wave Equation (2006) (14)
- Multilevel Monte Carlo Finite Element Methods for Stochastic Elliptic Variational Inequalities (2014) (14)
- Boundary layer resolution in hierarchical models of laminated composites (1994) (14)
- Finite elements with mesh refinement for elastic wave propagation in polygons (2016) (14)
- Electromagnetic wave scattering by random surfaces: uncertainty quantification via sparse tensor boundary elements (2016) (14)
- Compressed sensing Petrov-Galerkin approximations for parametric PDEs (2015) (14)
- A multiscale hp-FEM for 2D photonic crystal bands (2011) (14)
- Fully Discrete Multiscale Galerkin Bem Fully Discrete Multiscale Galerkin Bem (1995) (13)
- Sparse tensor finite elements for elliptic multiple scale problems (2011) (13)
- Discontinuous Galerkin FEM for Elliptic Problems in Polygonal Domains (2003) (13)
- Fast QMC Matrix-Vector Multiplication (2015) (13)
- Sparse, adaptive Smolyak algorithms for Bayesian inverse problems (2012) (12)
- Multi-level Monte Carlo Finite Difference and Finite Volume Methods for Stochastic Linear Hyperbolic Systems (2013) (12)
- Domain Uncertainty Quantification in Computational Electromagnetics (2020) (12)
- Intrinsic fault tolerance of multi level Monte Carlo methods (2012) (12)
- Multilevel QMC with Product Weights for Affine-Parametric, Elliptic PDEs (2018) (12)
- Covariance structure of parabolic stochastic partial differential equations (2012) (12)
- Exponential Convergence of Gauss-Jacobi Quadratures for Singular Integrals over Simplices in Arbitrary Dimension (2012) (12)
- Adaptive Galerkin approximation algorithms for Kolmogorov equations in infinite dimensions (2013) (12)
- Wavelet Galerkin BEM on Unstructured Meshes by Aggregation (2002) (12)
- Deep ReLU Neural Network Approximation for Stochastic Differential Equations with Jumps (2021) (12)
- Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations (2021) (12)
- Quasi-Monte Carlo finite element methods for elliptic PDEs with log-normal random coefficient (2013) (12)
- Wavelet-discretizations of parabolic integro-differential equations (2001) (12)
- Wavelet finite element method for option pricing in highdimensional di! usion market models (2010) (12)
- Compressive space-time Galerkin discretizations of parabolic partial differential equations (2015) (12)
- Finite Element Methods for Parabolic Problems (2013) (11)
- Exponential Convergence of hp-FEM for Elliptic Problems in Polyhedra: Mixed Boundary Conditions and Anisotropic Polynomial Degrees (2018) (11)
- Fully discrete multiscale Garlekin BEM (1995) (11)
- DeepCME: A deep learning framework for computing solution statistics of the chemical master equation (2021) (11)
- Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems (2021) (11)
- High Order SFV and Mixed SDG/FV Methods for the Uncertainty Quantification in Multidimensional Conservation Laws (2014) (11)
- Efficient Resolution of Anisotropic Structures (2014) (11)
- hp discontinuous Galerkin time stepping for parabolic problems (2000) (10)
- Constructive Deep ReLU Neural Network Approximation (2022) (10)
- The hp-version of the streamline diffusion finite element method in two space dimensions (2001) (10)
- Discontinuous Galerkin Methods for Acoustic Wave Propagation in Polygons (2018) (10)
- The hp streamline diffusion finite element method for convection dominated problems in one space dimension (1998) (10)
- High order Galerkin appoximations for parametric second order elliptic partial differential equations (2012) (10)
- Exponential convergence of hp FEM for spectral fractional diffusion in polygons (2020) (10)
- Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities (2020) (9)
- QMC Algorithms with Product Weights for Lognormal-Parametric, Elliptic PDEs (2016) (9)
- hp-DGFEM FOR KOLMOGOROV–FOKKER–PLANCK EQUATIONS OF MULTIVARIATE LÉVY PROCESSES (2012) (9)
- Adaptive anisotropic Petrov-Galerkin methods for first order transport equations (2016) (9)
- An Extraction Technique for Boundary Element Methods (1996) (9)
- Numerical Integration of Singular and Hypersingular Integrals in Boundary Element Methods (1992) (9)
- Advanced boundary element algorithms (1999) (9)
- Deep relu neural networks overcome the curse of dimensionality for partial integrodifferential equations (2021) (9)
- Monte-Carlo Finite-Volume Methods in Uncertainty Quantification for Hyperbolic Conservation Laws (2017) (8)
- Deep learning in high dimension: ReLU network Expression Rates for Bayesian PDE inversion (2020) (8)
- Approximation of Singularities by Quantized‐Tensor FEM (2015) (8)
- Covariance structure of parabolic stochastic partial differential equations (2013) (8)
- Quantized tensor FEM for multiscale problems: diffusion problems in two and three dimensions (2020) (8)
- Boundary layer resolution in hierarchical plate modelling (1995) (7)
- Variational sensitivity analysis of parametric Markovian market models (2008) (7)
- The method of arbitrary lines : an h-p error analysis for singular problems (1992) (7)
- Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 (2020) (7)
- Higher-order Quasi-Monte Carlo Training of Deep Neural Networks (2020) (7)
- Analyticity and sparsity in uncertainty quantification for PDEs with Gaussian random field inputs (2022) (7)
- Natural BEM for the electric field integral equation on polyhedra (2001) (7)
- Sparse Approximation Algorithms for High Dimensional Parametric Initial Value Problems (2012) (7)
- Sparse space‐time Galerkin BEM for the nonstationary heat equation (2013) (7)
- Symmetric Interior Penalty Discontinuous Galerkin Methods for Elliptic Problems in Polygons (2017) (7)
- Hp Finite Element Method for Convection-diiusion Problems (1997) (7)
- Regularity and generalized polynomial chaos approximation of parametric and random 2nd order hyperbolic partial differential equations (2011) (7)
- Weighted analytic regularity for the integral fractional Laplacian in polygons (2021) (7)
- Fast evaluation of nonlinear functionals of tensor product wavelet expansions (2011) (7)
- Analysis of a multilevel Markov chain Monte Carlo finite element method for Bayesian inversion of log-normal diffusions (2020) (7)
- Numerical approximation of statistical solutions of planar, incompressible flows (2016) (7)
- hp-dGFEM for Second-Order Elliptic Problems in Polyhedra I : Stability and Quasioptimality on Geometric Meshes (2009) (7)
- Quadrature algorithms for high dimensional singular integrands on simplices (2015) (7)
- Coupled Problems for Viscous Incompressible Flow in Exterior Domains (2002) (7)
- DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing (2021) (6)
- Convergent finite elements for a class of nonconvex variational problems (1998) (6)
- HIERARCHIC MODELS OF HELMHOLTZ PROBLEMS ON THIN DOMAINS (1998) (6)
- Exponential convergence in \(H^1\) of hp-FEM for Gevrey regularity with isotropic singularities (2019) (6)
- Multi-level Monte Carlo Finite Element method for parabolic stochastic partial differential equations (2011) (6)
- Numerical Analysis of Additive, Lévy and Feller Processes with Applications to Option Pricing (2010) (6)
- Multilevel approximation of Gaussian random fields: Covariance compression, estimation and spatial prediction (2021) (6)
- A note on sparse, adaptive Smolyak quadratures for Bayesian inverse problems (2013) (6)
- Multilevel Quasi-Monte Carlo Uncertainty Quantification for Advection-Diffusion-Reaction (2018) (5)
- Adaptive Galerkin approximation algorithms for partial differential equations in infinite dimensions (2012) (5)
- Analytic regularity for the incompressible Navier-Stokes equations in polygons (2020) (5)
- Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification (2018) (5)
- hp-FEM for second moments of elliptic PDEs with stochastic data (2010) (5)
- Quasi-Monte Carlo integration for affine-parametric, elliptic PDEs: local supports imply product weights (2016) (5)
- Finite Dimensional Approximations for Elliptic Problems with Rapidly Oscillating Coefficients (2002) (5)
- Analytic regularity of Stokes flow in polygonal domains (2002) (5)
- A Scalar BEM for Time Harmonic Eddy Current Problems with Impedance Boundary Conditions (2001) (5)
- A scalar boundary integrodifferential equation for eddy current problems using an impedance boundary condition (2001) (5)
- Exponential Convergence of hp -DGFEM for Elliptic Problems in Polyhedral Domains (2014) (5)
- High Order Generalized FEM For Lattice Materials (1999) (4)
- Two notes on the implementation of wavelet Galerkin boundary element methods (1997) (4)
- Multi-level Monte-Carlo finite element methods for stochastic elliptic variational inequalities (2013) (4)
- De Rham compatible Deep Neural Networks (2022) (4)
- Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier-Stokes Equations (2014) (4)
- Fully discrete hp-finite elements (1999) (4)
- Adaptive Hierarchic Modelling of Plates and Shells with A-Posteriori Error Estimation (1992) (4)
- hp-FEM for three-dimensional elastic plates (2002) (4)
- Sparse twisted tensor frame discretization of parametric transport operators (2011) (4)
- Stochastic Volatility Models with Jumps (2013) (4)
- Neural and gpc operator surrogates: construction and expression rate bounds (2022) (4)
- Exponential Convergence of hp FEM for the Integral Fractional Laplacian in Polygons (2022) (3)
- Extrapolated Lattice Rule Integration in Computational Uncertainty Quantification (2020) (3)
- Sparse Quadrature Approach to Bayesian Inverse Problems (2013) (3)
- Basket Option Pricing on Sparse Grids Using Fast Fourier Transforms (2007) (3)
- Analysis of multilevel MCMC-FEM for Bayesian inversion of log-normal diffusions (2019) (3)
- Galerkin least squares hp-finite element method for the Stokes problem (1998) (3)
- Numerical Simulations of High Current Arc in Circuit Breakers (2008) (3)
- On The Computation of Derivatives up to The Boundary and Recovery Techniques in BEM (1999) (3)
- hp-FEM for second moments of elliptic PDEs with stochastic data: part 1: analytic regularity (2010) (3)
- hp‐FEM for second moments of elliptic PDEs with stochastic data. II: Exponential convergence for stationary singular covariance functions (2012) (3)
- Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in L2(Rd, γd) (2021) (3)
- Realization of hp -Galerkin BEM in ℝ 3 (1996) (3)
- Binned Multilevel Monte Carlo for Bayesian Inverse Problems with Large Data (2016) (3)
- Multilevel Markov Chain Monte Carlo for Bayesian Inversion of Parabolic Partial Differential Equations under Gaussian Prior (2021) (3)
- On The Implementation Of A Fully DiscreteMultiscale Galerkin BEM (1970) (2)
- A Note On Variable Knot, Variable Order Composite Quadrature For Integrands With Power Singularities (1992) (2)
- Multilevel Monte Carlo approximations of statistical solutions to the Navier-Stokes equations (2013) (2)
- Convergence Rates of Sparse Tensor GPC FEM for Elliptic sPDEs (2011) (2)
- Elliptic Boundary Integral Equations (2010) (2)
- Wavelet solution of degenerate Kolmogoroff forward equations for exotic contracts in finance (2013) (2)
- Shape Holomorphy of the Calderón Projector for the Laplacian in $${\mathbb {R}}^2$$ (2021) (2)
- Exponential Convergence of Simplicial h p-FEM for H1-Functions with Isotropic Singularities (2015) (2)
- On the Numerical Integration of Singular Surface Integrals in the BEM (1992) (2)
- Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D (2022) (2)
- hp‐FEM for second moments of elliptic PDEs with stochastic data. I. Analytic regularity (2012) (2)
- Multi-asset Options (2013) (2)
- Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification (2022) (2)
- Exponential convergence of (2018) (2)
- Multilevel Monte Carlo FEM for Elliptic PDEs with Besov Random Tree Priors (2023) (2)
- hp-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains (2020) (2)
- Hierarchic Models of Vibration Problems on Thin Domains (1998) (2)
- Mixed hp-finite element approximations on geometric boundary layer meshes in R3 (2001) (2)
- Exponential convergence of mixed hp-DGFEM for the incompressible Navier–Stokes equations in ℝ2 (2020) (2)
- Locking Effects for the Reissner-Mindlin Plate Model (1992) (2)
- Applications of Mathematics (2006) (1)
- Quadrature for hp Galerkin BEM in lR (2004) (1)
- Correction to: Multilevel Monte Carlo front-tracking for random scalar conservation laws (2018) (1)
- Hp90: a General & Exible Fortran 90 Hp-fe Code Hp90: a General & Exible Fortran 90 Hp-fe Code (1)
- Uncertainty Quantification for Spectral Fractional Diffusion: Sparsity Analysis of Parametric Solutions (2018) (1)
- Multi-level Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic PDEs with Random Coefficients (2015) (1)
- Exponential convergence of simplicial hp-FEM for H^1-functions with isotropic singularities (2014) (1)
- Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions (2017) (1)
- Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in $L^2(\mathbb{R}^d,\gamma_d)$ (2021) (1)
- Fast Numerical Solution of the Vector Molodensky Problem (2001) (1)
- Exponential Convergence of hp-Time-Stepping in Space-Time Discretizations of Parabolic PDEs (2022) (1)
- Multilevel QMC Uncertainty Quantification for Advection-Reaction-Diffusion (2019) (1)
- Deep solution operators for variational inequalities via proximal neural networks (2022) (1)
- Recent progress in theory and applications : foundations, trees and numerical issues in finance (2010) (1)
- ANISOTROPIC STABLE LEVY COPULA PROCESSES — ANALYTICAL AND NUMERICAL ASPECTS (2007) (1)
- Stable and stabilized hp -finite element methods for the Stokes problem (2000) (1)
- Parallelization of a Radiative Transfer Solver (2012) (1)
- Micro-Mechanical Modelling of the Entanglement of Carbon Fiber Tows (2017) (1)
- NUMERICAL ANALYSIS OF LOGNORMAL DIFFUSIONS ON S 2 (2016) (1)
- Tensor Rank bounds for Point Singularities in $\mathbb{R}^3$ (2019) (1)
- A multiscale hp-FEM for 2D photonic crystal band (2010) (1)
- Simulation of large deformations in shell structures by the p-version of the finite element method (2001) (1)
- Hierarchic Modelling in Elasticity by generalized p- and hp-FEM (2005) (1)
- Fem for Reaction-diiusion Equations Ii: Regularity Seminar F Ur Angewandte Mathematik Eidgenn Ossische Technische Hochschule Ch-8092 Z Urich Switzerland Hp Fem for Reaction-diiusion Equations Ii: Regularity (1997) (1)
- Higher Order Quasi Monte-Carlo Integration in Uncertainty Quantification (2014) (1)
- Space–time hp-approximation of parabolic equations (2018) (0)
- The Hp Streamline Diiusion Finite Element Method for Convection Dominated Problems in One Space Dimension the Hp Streamline Diiusion Finite Element Method for Convection Dominated Problems in One Space Dimension (1998) (0)
- ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! (2009) (0)
- MLQMC with product weights for elliptic PDEs with lognormal coefficients parametrized in multiresolution representations (2017) (0)
- Elements of Numerical Methods for PDEs (2013) (0)
- Correction to: Multilevel Monte Carlo front-tracking for random scalar conservation laws (2017) (0)
- Stochastic Volatility Models (2013) (0)
- Solution of Linear Systems of Equations (2010) (0)
- A scalar boundary integrodifferential equation for eddy current problems using an impedance bound condition (2000) (0)
- Subspace Correction Methods for the Iterative Solution of Hierarchic Plate Models. 1: Heat Transfer Problems (1994) (0)
- TWO-SCALE FEM FOR HOMOGENIZATION (0)
- Multiresolution kernel matrix algebra (2022) (0)
- Large deformation shape uncertainty quantification in acoustic scattering (2018) (0)
- Generating the Matrix Coefficients (2010) (0)
- Discontinuous Galerkin time stepping methods for parabolic problems (2000) (0)
- Hierachical Modeling and Locking Effects in the Numerical Analysis of Multistructures. (1995) (0)
- Hierarchical hp Modeling and Locking Resolution in Laminated Plates and Shells. (1998) (0)
- Deep ReLU neural network expression for elliptic multiscale problems (2020) (0)
- A P ] 8 F eb 2 01 2 Sparse Deterministic Approximation of Bayesian Inverse Problems (0)
- Interest Rate Models (2013) (0)
- FINITE ELEMENT BASED SECOND MOMENT ANALYSIS FOR ELLIPTIC PROBLEMS WITH STOCHASTIC INPUT DATA (2008) (0)
- Multilevel Monte Carlo front-tracking for random scalar conservation laws (2015) (0)
- QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights (2018) (0)
- Lévy Matters I - ReadingSample (2017) (0)
- WORKING GROUPS PDE (2010) (0)
- EXPONENTIAL CONVERGENCE OF GAUSS-JACOBI QUADRATURES FOR SINGULAR INTEGRALS OVER HIGH DIMENSIONAL SIMPLICES (2010) (0)
- Multilevel Domain Uncertainty Quantification in Computational Electromagnetics (2022) (0)
- Numerical Analysis of Hyperbolic PDEs Handout (2009) (0)
- Application of QMC methods to PDEs with random coefficients : a survey of analysis and implementation (2016) (0)
- Analytical and Numerical Aspects (2006) (0)
- ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! (2010) (0)
- UvA-DARE ( Digital Academic Repository ) Space-time variational saddle point formulations of Stokes and Navier-Stokes equations (2014) (0)
- Multidimensional Lévy Models (2013) (0)
- Multiwavelets for Second Kind Integral Equations Multiwavelets for Second Kind Integral Equations (1997) (0)
- De Rham compatible Deep Neural Network FEM (2022) (0)
- Sensitivities and Greeks (2013) (0)
- ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! (2010) (0)
- Discontinuous Galerkin Methods for Acoustic Wave Propagation in Polygons (2018) (0)
- QTT-finite-element approximation for multiscale problems I: model problems in one dimension (2016) (0)
- Fast numerical methods for non-local operators (2004) (0)
- ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! (2010) (0)
- Convergence Rates of space-time FEM for Wave Equation in Polygons (2017) (0)
- Exploiting Sparsity in Bayesian Inverse Problems of Parametric Operator Equations (2014) (0)
- Exponential Convergence of hp-FEM for Elliptic Problems in Polyhedra: Mixed Boundary Conditions and Anisotropic Polynomial Degrees (2017) (0)
- Workshop on Mathematics of Deep Learning (2017) (0)
- Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs (2019) (0)
- European Options in BS Markets (2013) (0)
- J finite element method for problems in mechanics with boundary layers (0)
- Monte Carlo convergence rates for kth moments in Banach spaces (2022) (0)
- A spectral Garlekin method for hydrodynamic stability problems (1998) (0)
- Crystal structure and Hirshfeld surface analysis of N-{[diphenyl(vinyl)silyl]methyl}-2-methylpropan-2-ammonium chloride (2022) (0)
- Deep Learning in High Dimension: Neural Network Expression Rates for Analytic Functions in \(\pmb{L^2(\mathbb{R}^d,\gamma_d)}\) (2023) (0)
- Quasi Monte-Carlo Integration for Parametric and Stochastic Operator Equations (2013) (0)
- Mixed Potential Gas Sensor with Au,Pt-YSZ Electrode for Optimization of Wood Combustion Processes: Validation of a Signal Stabilization Concept By Repeated Electrochemical Treatments (2020) (0)
- A-posteriori QMC-FEM error estimation for Bayesian inversion and optimal control with entropic risk measure (2023) (0)
- A Posteriori Error Estimation (2010) (0)
- MAXWELL EIGENVALUES ANDDISCRETE COMPACTNESS INTWO (0)
- Hp Fem for Reaction-diiusion Equations I: Robust Exponential Convergence Seminar F Ur Angewandte Mathematik Eidgenn Ossische Technische Hochschule Ch-8092 Z Urich Switzerland Hp Fem for Reaction-diiusion Equations I: Robust Exponential Convergence (1997) (0)
- Convergence Rates of Sparse Tensor Discretizations for PDEs with Stochastic Data (2010) (0)
- Numerical Simulation of Compressible Magnetohydrodynamic Plasma Flow in a Curcuit Breaker (2008) (0)
- Multidimensional Diffusion Models (2013) (0)
- Multidimensional Feller Processes (2013) (0)
- High order approximations for hyperbolic conservation laws with random initial data (2012) (0)
- A Spectral Galerkin Method for Hydrodynamic StabilityProblemsN (0)
- A P-FEM APPROACH TO SOLVE THE ORR-SOMMERFELD EQUATION (1999) (0)
- Notions of Mathematical Finance (2013) (0)
- ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! (2010) (0)
- High-order finite element approximation for partial differential equations (2014) (0)
- Numerical Treatment of Differential and Integral Equations by the P and H-P Versions of the Finite Element Method (1992) (0)
- p-Parametric Surface Approximation (2010) (0)
- Multilevel Monte Carlo method for parabolic stochastic partial differential equations (2012) (0)
- ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! (2009) (0)
- Galerkin discretization of parametric operator equations (2012) (0)
- Multilevel Monte-Carlo Methods for hyperbolic PDEs with random input data (2014) (0)
- Generalized P-fem in Homogenization Generalized P-fem in Homogenization (1999) (0)
- Abstracts in Chronological Order Multi-Index Finite Element Method (2019) (0)
- DeepCME: A deep learning framework for solving the Chemical Master Equation (2021) (0)
- Galerkin Least Squares Hp-fem for the Stokes Problem Galerkin Least Squares Hp-fem Pour Le Probl Eme De Stokes (2007) (0)
- The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem (2013) (0)
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