Unconditional energy stability analysis of a second order implicit-explicit local discontinuous Galerkin method for the Cahn-Hilliard equation (Q1691418)

This paper focuses on the numerical solution of the Cahn-Hilliard equation, which describes the phase separation phenomenon. This equation is numerically approximated with the aid of a second-order in time implicit-explicit local discontinuous Galerkin method. The well-known fact that a nonlinear stability property is guaranted for any solution of the Cahn-Hilliard equation is extended also for the discretized scheme. The discretized Cahn-Hilliard system is shown to inherit the nonlinear stability of the continuous model under a condition of a suitable stabilization technique applied. In this case an unconditional energy stability of the scheme is proven. Numerical experiments are performed to support the analysis.