Stability of the Semi-Implicit Method for the Cahn-Hilliard Equation with Logarithmic Potentials

We consider the two-dimensional Cahn-Hilliard equation with logarithmic potentials and periodic boundary conditions.We employ the standard semi-implicit numerical scheme,which treats the linear fourth-order dissipation term implicitly and the nonlinear term explicitly.Under natural constraints on the time step we prove strict phase separation and energy stability of the semiimplicit scheme.This appears to be the first rigorous result for the semi-implicit discretization of the Cahn-Hilliard equation with singular potentials.