Multilevel quasi-Monte Carlo integration with product weights for elliptic PDEs with lognormal coefficients

DOI10.1051/m2an/2019016OpenAlexW2943717311WikidataQ114105463 ScholiaQ114105463MaRDI QIDQ4972102

Lukas Herrmann, Christoph Schwab

Publication date: 22 November 2019

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/6223e50bb21954f39a0a79582f2351b805380c6e

zbMATH Keywords

error estimatesquasi-Monte Carlo methodsuncertainty quantificationhigh-dimensional quadratureelliptic partial differential equations with lognormal inputmultilevel quasi-Monte Carlo

Mathematics Subject Classification ID

Random fields (60G60) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical integration (65D30)

Related Items

MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM, Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification, Goal-oriented adaptive finite element multilevel Monte Carlo with convergence rates, Convergence of a stochastic collocation finite volume method for the compressible Navier-Stokes system, Suboptimality of Gauss–Hermite Quadrature and Optimality of the Trapezoidal Rule for Functions with Finite Smoothness, Multilevel approximation of Gaussian random fields: Fast simulation, Analyticity of parametric elliptic eigenvalue problems and applications to quasi-Monte Carlo methods, Multilevel Quasi-Monte Carlo Uncertainty Quantification for Advection-Diffusion-Reaction, Multilevel QMC with Product Weights for Affine-Parametric, Elliptic PDEs, QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights, Strong convergence analysis of iterative solvers for random operator equations, Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems, Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations, Multilevel Quasi Monte Carlo Methods for Elliptic PDEs with Random Field Coefficients via Fast White Noise Sampling

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