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

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.

Keywords:

• Finite element
• Stochastic PDEs
• White noise
• Wiener–Itô chaos coefficients

Additional information

Notes on contributors

H. Manouzi

Email: [email protected]