Energy Stable Finite Element/Spectral Method for Modified Higher-Order Generalized Cahn-Hilliard Equations

摘要

Our aim in this paper is to study a fully discrete scheme for modified higher-order(in space)anisotropic generalized Cahn-Hilliard models which have extensive applications in biology,image processing,etc.In particular,the scheme is a combina-tion of finite element or spectral method in space and a second-order stable scheme in time.We obtain energy stability results,as well as the existence and uniqueness of the numerical solution,both for the space semi-discrete and fully discrete cases.We also give several numerical simulations which illustrate the theoretical results and,espe-cially,the effects of the higher-order terms on the anisotropy.