Finite element approximations for a linear fourth-order parabolic SPDE in two and three space dimensions with additive space–time white noise

Abstract

We consider an initial and Dirichlet boundary value problem for a linear fourth-order stochastic parabolic equation, in two or three space dimensions, forced by an additive space–time white noise. Discretizing the space–time white noise a modeling 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 standard Galerkin finite element method based on H2-piecewise polynomials, and, for time-stepping, the Backward Euler method. We derive strong a priori estimates for the modeling error and for the approximation error to the solution of the regularized problem.