SPD

Abstract

We study the Cahn-Hilliard equation perturbed by additive colored noise also known as the Cahn-Hilliard-Cook equation. 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. This is joint work with Mihaly Kovacs, University of Otago, New Zealand, and Ali Mesforush, Chalmers University of Technology, Sweden.