SPDEs driven by additive and multiplicative white noises: A numerical study

In this paper we present a finite element approximation of a model of a linear stochastic partial differential equation driven by additive and multiplicative white noises. 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. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.