On the convergence of the stochastic Galerkin method for random elliptic partial differential equations

DOI10.1051/m2an/2013066zbMath1297.65010OpenAlexW2092478820MaRDI QIDQ5397514

Antje Mugler, H.-J. Starkloff

Publication date: 24 February 2014

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

Full work available at URL: https://doi.org/10.1051/m2an/2013066

zbMATH Keywords

convergencefinite elementrandom fieldspectral methodsstochastic Galerkin methodgeneralized polynomial chaosstochastic variational problemelliptic partial differential equation with random coefficientsstochastic Petrov-Galerkin method

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

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Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs ⋮ Subordinated Gaussian random fields in elliptic partial differential equations ⋮ Unnamed Item ⋮ Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems ⋮ Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs) ⋮ Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations ⋮ On expansions and nodes for sparse grid collocation of lognormal elliptic PDEs ⋮ A Convex Optimization Framework for the Inverse Problem of Identifying a Random Parameter in a Stochastic Partial Differential Equation ⋮ Multilevel Monte Carlo estimators for elliptic PDEs with Lévy-type diffusion coefficient

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