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Sparse Quadrature as an Alternative to Monte Carlo for Stochastic Finite Element Techniques
Author(s) -
Keese A.,
Matthies H. G.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310516
Subject(s) - monte carlo method , mathematics , quasi monte carlo method , monte carlo integration , quadrature (astronomy) , galerkin method , finite element method , discontinuous galerkin method , nonlinear system , stochastic partial differential equation , partial differential equation , hybrid monte carlo , monte carlo molecular modeling , statistical physics , mathematical optimization , mathematical analysis , markov chain monte carlo , physics , statistics , optics , thermodynamics , quantum mechanics
We consider the solution of nonlinear stochastic partial differential equations by a Galerkin‐method and by projection in the stochastic dimension and compute the occurring high‐dimensional integrals by sparse (Smolyak)‐ and Monte Carlo‐integration.