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

Keese, A.; Matthies, H. G.

PAMM, Proc. Appl. Math. Mech. 3, 493-494 (2003).

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