Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs

DOI10.1051/m2an/2021017OpenAlexW3153006547WikidataQ114105435 ScholiaQ114105435MaRDI QIDQ5154014

Dinh Dung

Publication date: 1 October 2021

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

Full work available at URL: https://arxiv.org/abs/1904.06502

zbMATH Keywords

high-dimensional approximationcollocation approximationparametric and stochastic elliptic PDEsfully discrete non-adaptive integrationfully discrete non-adaptive polynomial interpolation approximationlognormal inputs

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical interpolation (65D05) Numerical solutions to stochastic differential and integral equations (65C30) Numerical quadrature and cubature formulas (65D32)

Related Items (4)

Erratum to: “Sparse-grid polynomial interpolation approximation and integration for parametric and stochastic elliptic PDEs with lognormal inputs” ⋮ Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs ⋮ Collocation approximation by deep neural ReLU networks for parametric and stochastic PDEs with lognormal inputs ⋮ Suboptimality of Gauss–Hermite Quadrature and Optimality of the Trapezoidal Rule for Functions with Finite Smoothness

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