Energy Stable Finite Element/Spectral Method for Modified Higher-Order Generalized Cahn-Hilliard Equations (Journal of Mathematical Study, 2018)
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 extensiveapplications in biology, image processing, etc. In particular, the scheme is a combinationof finite element or spectral method in space and a second-order stable scheme intime. We obtain energy stability results, as well as the existence and uniqueness of thenumerical solution, both for the space semi-discrete and fully discrete cases. We alsogive several numerical simulations which illustrate the theoretical results and, especially,the effects of the higher-order terms on the anisotropy.
Keywords: Modified Cahn-Hilliard equation; higher-order models; energy stability; anisotropy.