Volume 51, Issue 3
Energy Stable Finite Element/Spectral Method for Modified Higher-Order Generalized Cahn-Hilliard Equations

Hongyi Zhu, Laurence Cherfil, Alain Miranville, Shuiran Peng & Wen Zhang

J. Math. Study, 51 (2018), pp. 253-293.

Published online: 2018-08

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  • Abstract

Our aim in this paper is to study a fully discrete scheme for modified higherorder (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.

  • Keywords

Modified Cahn-Hilliard equation higher-order models energy stability anisotropy

  • AMS Subject Headings

35K55 35J60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hyzhu@stu.xmu.edu.cn (Hongyi Zhu)

laurence.cherfils@univ-lr.fr (Laurence Cherfil)

alain.miranville@math.univ-poitiers.fr (Alain Miranville)

Shuiran.Peng@math.univ-poitiers.fr (Shuiran Peng)

zhangwenmath@126.com (Wen Zhang)

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@Article{JMS-51-253, author = {Zhu , Hongyi and Cherfil , Laurence and Miranville , Alain and Peng , Shuiran and Zhang , Wen }, title = {Energy Stable Finite Element/Spectral Method for Modified Higher-Order Generalized Cahn-Hilliard Equations}, journal = {Journal of Mathematical Study}, year = {2018}, volume = {51}, number = {3}, pages = {253--293}, abstract = {

Our aim in this paper is to study a fully discrete scheme for modified higherorder (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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v51n3.18.02}, url = {http://global-sci.org/intro/article_detail/jms/12657.html} }
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