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

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

Author Details

Hongyi Zhu

Laurence Cherfils

Alain Miranville

Shuiran Peng

Wen Zhang

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