A new projection scheme for linear stochastic systems

In this paper we present a new projection scheme for solving linear stochastic partial differential equations. The solution process is approximated using a set of basis vectors spanning a preconditioned stochastic Krylov subspace. We propose a strong Galerkin condition which ensures that the stochastic residual error is orthogonal to the approximating subspace with probability one. We present numerical studies for a model problem in stochastic structural mechanics to demonstrate that the proposed strong Galerkin projection scheme gives better results that the weak Galerkin scheme