Finite Element Approximation of the Cahn-Hilliard-Cook equation

We study the nonlinear stochastic Cahn-Hilliard equation per- turbed by additive colored noise. We show almost sure existence and regularity of solutions. We introduce spatial approximation by a standard finite element method and prove error estimates of optimal order on sets of probability arbitrarily close to 1. We also prove strong convergence without known rate.