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 and Wen Zhang

10.4208/jms.v51n3.18.02

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

Full Article 22 93
  • 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.

  • History

Submitted: 2018-08

Accepted: 2019-03

Published online: 2018-08

  • AMS Subject Headings

35K55, 35J60

  • Cited by