Application of the Local Discontinuous Galerkin Method for the Allen-Cahn/Cahn-Hilliard System

Abstract

In this paper, we consider the application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system. The method in this paper extends the local discontinuous Galerkin method in [10] to the more general application system which is coupled with the Allen-Cahn and Cahn-Hilliard equations. Similar energy stability result as that in [10] is presented. Numerical results for the nonlinear problems which include the Allen-Cahn/Cahn-Hilliard system for one-dimensional and two-dimensional cases demonstrate the accuracy and capability of the numerical method.