TY - JOUR
T1 - Energy Stable Finite Element/Spectral Method for Modified Higher-Order Generalized Cahn-Hilliard Equations
AU - Zhu , Hongyi
AU - Cherfils , Laurence
AU - Miranville , Alain
AU - Peng , Shuiran
AU - Zhang , Wen
JO - Journal of Mathematical Study
VL - 3
SP - 253
EP - 293
PY - 2018
DA - 2018/08
SN - 51
DO - http://doi.org/10.4208/jms.v51n3.18.02
UR - https://global-sci.org/intro/article_detail/jms/12657.html
KW - Modified Cahn-Hilliard equation, higher-order models, energy stability, anisotropy.
AB - <p style="text-align: justify;">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.</p>