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

Authors:
Georgios T. Kossioris;Georgios E. Zouraris
Affiliations:
Department of Mathematics, University of Crete, GR-714 09 Heraklion, Crete, Greece;Department of Mathematics, University of Crete, GR-714 09 Heraklion, Crete, Greece
Venue:
Applied Numerical Mathematics
Year:
2013

Citing 3
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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 H^2-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.