Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise

Kossioris, Georgios T.; Zouraris, Georgios E.

ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 2, pp. 289-322.

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 C⁰ or C¹ 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.

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