TY - JOUR T1 - Energy Stable Finite Element/Spectral Method for Modified Higher-Order Generalized Cahn-Hilliard Equations AU - Zhu , Hongyi AU - Cherfils , Laurence AU - Miranville , Alain AU - Peng , Shuiran AU - Zhang , Wen JO - Journal of Mathematical Study VL - 3 SP - 253 EP - 293 PY - 2018 DA - 2018/08 SN - 51 DO - http://doi.org/10.4208/jms.v51n3.18.02 UR - https://global-sci.org/intro/article_detail/jms/12657.html KW - Modified Cahn-Hilliard equation, higher-order models, energy stability, anisotropy. AB -

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 combination 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, especially, the effects of the higher-order terms on the anisotropy.