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 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. |