A discontinuous Galerkin method for stochastic Cahn–Hilliard equations

Abstract

In this paper, a discontinuous Galerkin method for the stochastic Cahn-Hilliard equation with additive random noise, which preserves the conservation of mass, is investigated. Numerical analysis and error estimates are carried out for the linearized stochastic Cahn-Hilliard equation. The effects of the noises on the accuracy of our scheme are also presented. Numerical examples simulated by Monte Carlo method for both linear and nonlinear stochastic Cahn-Hilliard equations are presented to illustrate the convergence rate and validate our conclusion.