  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 H2-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.
