A finite element approximation of linear stochastic PDEs driven by multiplicative white noise

Authors:
H. Manouzi
Affiliations:
Department of Mathematics and Statistic, Laval University, Quebec, Canada
Venue:
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
Year:
2008

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Abstract

In this paper we present a finite element approximation of linear stochastic PDEs driven by multiplicative white noise. Using the Wick-product properties and the Wiener-Itô chaos expansion, the stochastic variational problem is reformulated as a set of deterministic variational problems. To obtain the chaos coefficients in the corresponding deterministic equations, we use the usual Galerkin finite element method using standard techniques. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.