# American Institute of Mathematical Sciences

September  2013, 18(7): 1845-1872. doi: 10.3934/dcdsb.2013.18.1845

## Finite element approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise

 1 Department of Mathematics, University of Crete, P.O. Box 2208, GR-710 03 Heraklion, Crete, Greece, Greece

Received  July 2012 Revised  April 2013 Published  May 2013

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 stochastic parabolic problem discretizing the noise using linear splines. Then we construct fully-discrete approximations to the solution of the approximate problem 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. We derive strong a priori estimates: for the error between the solution to the problem and the solution to the approximate problem, and for the numerical approximation error of the solution to the approximate problem.
Citation: Georgios T. Kossioris, Georgios E. Zouraris. Finite element approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1845-1872. doi: 10.3934/dcdsb.2013.18.1845
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##### References:
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