Volume 44, Number 2, March-April 2010
|Page(s)||289 - 322|
|Published online||27 January 2010|
Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise
Department of Mathematics, University of Crete, 714 09
Heraklion, Crete, Greece and Institute of Applied and
Computational Mathematics, FO.R.T.H., 711 10 Heraklion, Crete,
Greece. email@example.com; firstname.lastname@example.org
Revised: 20 May 2009
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.
Mathematics Subject Classification: 65M60 / 65M15 / 65C20
Key words: Finite element method / space-time white noise / Backward Euler time-stepping / fully-discrete approximations / a priori error estimates
© EDP Sciences, SMAI, 2010
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