In this article, we present a second-order in time implicit-explicit
(IMEX) local discontinuous Galerkin (LDG) method for
computing the Cahn-Hilliard equation, which describes the
phase separation phenomenon. It is well-known that
the Cahn-Hilliard equation has a nonlinear stability property, i.e.,
the free-energy functional decreases with respect to time. The
discretized Cahn-Hilliard system modeled by the IMEX
LDG method can inherit the nonlinear stability of the
continuous model. We apply a stabilization technique and prove
unconditional energy stability of our scheme.
Numerical experiments are performed to validate the analysis.
Computational efficiency can be
significantly enhanced by using this IMEX LDG method with a large
time step.