Numerical Solution for Random Forced SPDE via Galerkin Finite Element Method

In this paper, we present a deterministic finite element approach for solving a random forced Diffusion equation. Separation of random and deterministic variables is done by Karhunen- Loeve expansion. Truncating the Karhunen-Loeve expansion of the permeability field leads to a finite dimensional approximation of the problem. The problem is discretized, in spatial part, using the finite-element method and the polynomial chaos expansion in stochastic part. Finally, using Kronecker product preconditioner and thus, preconditioned conjugate gradient method the governed system of equation is solved. Numerical experiments are presented for illustrating the theoretical results.