FULLY-DISCRETE FINITE ELEMENT APPROXIMATIONS FOR A FOURTH-ORDER LINEAR STOCHASTIC PARABOLIC EQUATION WITH ADDITIVE SPACE-TIME WHITE NOISE

We consider an initial and Dirichlet boundary value problem for a fourth-order linear stochastic parabolic equation, in one space dimension, forced by an additive space-time white noise. Discretizing the space-time white noise a modelling error is introduced and a regularized fourth-order linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the regularized problem are constructed by using, for discretization in space, a Galerkin finite element method based on C-0 or C-1 piecewise polynomials, and, for time-stepping, the Backward Euler method. We derive strong a priori estimates for the modelling error and for the approximation error to the solution of the regularized problem.