Energy Stable Finite Element/Spectral Method for Modified Higher-Order Generalized Cahn-Hilliard Equations
Year: 2018
Author: Hongyi Zhu, Laurence Cherfils, Alain Miranville, Shuiran Peng, Wen Zhang
Journal of Mathematical Study, Vol. 51 (2018), Iss. 3 : pp. 253–293
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v51n3.18.02
Journal of Mathematical Study, Vol. 51 (2018), Iss. 3 : pp. 253–293
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 41
Keywords: Modified Cahn-Hilliard equation higher-order models energy stability anisotropy.