Efficient Energy Stable Schemes with Spectral Discretization in Space for Anisotropic Cahn–hilliard Systems

We develop in this paper efficient and robust numerical methods for solving anisotropic Cahn–Hilliard systems. We construct energy stable schemes for the time discretization of the highly nonlinear anisotropic Cahn-Hilliard systems by using a stabilization technique. At each time step, these schemes lead to a sequence of linear coupled elliptic equations with constant coefficients which can be efficiently solved by using a spectral-Galerkin method. We present numerical results which are consistent with earlier work on this topic, and also carry out various simulations, such as the linear biLaplacian regularization and the nonlinear Willmore regularization, to demonstrate the efficiency and robustness of the new schemes.