Local discontinuous Galerkin methods for the Cahn–Hilliard type equations

In this paper, we develop local discontinuous Galerkin (LDG) methods for the fourth order nonlinear Cahn-Hilliard equation and system. The energy stability of the LDG methods is proved for the general nonlinear case. Numerical examples for the Cahn-Hilliard equation and the Cahn-Hilliard system in one and two dimensions are presented and the numerical results illustrate the accuracy and capability of the methods.