Finite Element Approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise

Kossioris, Georgios and Zouraris, Georgios (2013) Finite Element Approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 18 (7). pp. 1845-1872. ISSN 1531-3492

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Abstract

We consider an initial- and Dirichlet boundary- value problem for a linear Cahn-Hilliard-Cook equation, in one space dimension, forced by the space derivative of a space-time white noise. First, we propose an approximate regularized stochastic parabolic problem discretizing the noise using linear splines. Then fully-discrete approximations to the solution of the regularized problem are constructed using, for the discretization in space, a Galerkin finite element method based on $H^2-$piecewise polynomials, and, for time-stepping, the Backward Euler method. Finally, we derive strong a priori estimates for the modeling error and for the numerical approximation error to the solution of the regularized problem.

Item Type: Article
Subjects: Q Science > QA Mathematics
Depositing User: Dr Georgios Zouraris
Date Deposited: 09 Dec 2013 11:58
Last Modified: 16 May 2015 18:03
URI: http://preprints.acmac.uoc.gr/id/eprint/250

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