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
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.
DOI : https://doi.org/10.1051/m2an/2010003
Classification:  65M60,  65M15,  65C20
@article{M2AN_2010__44_2_289_0,
author = {Kossioris, Georgios T. and Zouraris, Georgios E.},
title = {Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {44},
number = {2},
year = {2010},
pages = {289-322},
doi = {10.1051/m2an/2010003},
zbl = {1189.65018},
mrnumber = {2655951},
language = {en},
url = {http://http://www.numdam.org/item/M2AN_2010__44_2_289_0}
}

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, pp. 289-322. doi : 10.1051/m2an/2010003. http://www.numdam.org/item/M2AN_2010__44_2_289_0/

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