Local discontinuous Galerkin methods with implicit-explicit multistep time-marching for solving the nonlinear Cahn-Hilliard equation

Abstract

In this paper, we develop the fully discrete local discontinuous Galerkin (LDG) methods coupled with the implicit-explicit (IMEX) multistep time marching for solving the nonlinear Cahn-Hilliard equation. To be more specific, we rewrite the Cahn-Hilliard equation in a novel form by adding and subtracting a “linear” term. Then we discretize the spatial derivatives with the LDG methods and the temporal derivative with the IMEX multistep method. Finally, a series of numerical experiments are given to verify the accuracy, efficiency and validness of proposed method.