Unconditionally energy stable discontinuous Galerkin schemes for the Cahn–Hilliard equation

In this paper, we introduce novel discontinuous Galerkin (DG) schemes for the Cahn-Hilliard equation, which arises in many applications. The method is designed by integrating mixed DG spatial discretization with \emph{Invariant Energy Quadratization} (IEQ) approach time discretization. Coupled a projection, resulting IEQ-DG are shown to be unconditionally energy dissipative, and can efficiently solved without resorting any iteration method. Both one two dimensional numerical examples provided verify theoretical results, demonstrate good performance of terms efficiency, accuracy, preservation desired solution properties.