Kossioris, Georgios T.; Zouraris, Georgios E.
Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) no. 2 , p. 289-322
Zbl 1189.65018 | MR 2655951
doi : 10.1051/m2an/2010003
URL stable : http://www.numdam.org/item?id=M2AN_2010__44_2_289_0

Classification:  65M60,  65M15,  65C20
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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