A long-time stable fully discrete approximation of the Cahn-Hilliard equation with inertial term

Abstract : We prove the Lyapunov stability of a time and space discretization of the Cahn-Hilliard equation with inertial term. The space discretization is a mixed (or "splitting" finite element method with numerical integration which includes a standard finite difference approximation. The time discretization is the backward Euler scheme. The smallness assumption on the time step does not depend on the mesh step.