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Sparse quadrature as an alternative to Monte Carlo for stochastic finite element techniques. (English) Zbl 1354.65013

Summary: 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.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
65D30 Numerical integration
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65C05 Monte Carlo methods
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