TY - JOUR T1 - Efficient Energy Stable Schemes with Spectral Discretization in Space for Anisotropic Cahn-Hilliard Systems JO - Communications in Computational Physics VL - 5 SP - 1189 EP - 1208 PY - 2013 DA - 2013/05 SN - 13 DO - http://doi.org/10.4208/cicp.101111.110512a UR - https://global-sci.org/intro/article_detail/cicp/7270.html KW - AB -

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 that can be efficiently solved by using a spectral-Galerkin method. We present numerical results that are consistent with earlier work on this topic, and also carry out various simulations, such as the linear bi-Laplacian regularization and the nonlinear Willmore regularization, to demonstrate the efficiency and robustness of the new schemes.