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.