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Fully-discrete finite element approximationsfora fourth-order linear stochastic parabolic equationwith additive space-time white noise

Published online by Cambridge University Press:  27 January 2010

Georgios T. Kossioris  and
Georgios E. Zouraris
Georgios T. Kossioris
Affiliation:
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 protected]; [email protected]
Georgios E. Zouraris
Affiliation:
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 protected]; [email protected]
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Abstract

We consider an initial and Dirichlet boundary value problem fora fourth-order linear stochastic parabolic equation, in one spacedimension, forced by an additive space-time white noise.Discretizing the space-time white noise a modelling error isintroduced and a regularized fourth-order linear stochasticparabolic problem is obtained. Fully-discrete approximations to the solution of the regularizedproblem are constructed by using, for discretization in space, aGalerkin finite element method based on C0 or C1piecewise polynomials, and, for time-stepping, the Backward Eulermethod.We derive strong a priori estimates for the modelling error and forthe approximation error to the solution of the regularizedproblem.

Keywords

Finite element methodspace-time white noiseBackwardEuler time-steppingfully-discrete approximationsa priori errorestimates
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 2 , March 2010 , pp. 289 - 322
Copyright
© EDP Sciences, SMAI, 2010

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