ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS

DOI10.1142/S0218202512500236zbMath1262.65009OpenAlexW2056227133MaRDI QIDQ3166761

Fabio Nobile, Raúl Tempone, Joakim Beck, Lorenzo Tamellini

Publication date: 15 October 2012

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202512500236

zbMATH Keywords

convergence numerical examples sparse grids uncertainty quantification multivariate polynomial approximation linear elliptic equations stochastic coefficients stochastic collocation methods stochastic Galerkin methods Smolyak approximation best M-terms polynomial approximation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) 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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