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We consider a model initial- and Dirichlet boundary- value problem for alinearized Cahn-Hilliard-Cook equation, in one space dimension, forced by thespace derivative of a space-time white noise. First, we introduce a canvasproblem the solution to which is a regular approximation of the mild solutionto the problem and depends on a finite number of random variables. Then,fully-discrete approximations of the solution to the canvas problem areconstructed using, for discretization in space, a Galerkin finite elementmethod based on $H^2$ piecewise polynomials, and, for time-stepping, animplicit/explicit method. Finally, we derive a strong a priori estimate of theerror approximating the mild solution to the problem by the canvas problemsolution, and of the numerical approximation error of the solution to thecanvas problem.

An IMEX Finite Element Method for a linearized Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise