A finite element method for Allen-Cahn equation on deforming surface

doi:10.1016/j.camwa.2021.03.018

CSpace

	A finite element method for Allen-Cahn equation on deforming surface
	Olshanskii, Maxim 1; Xu, Xianmin 2; Yushutin, Vladimir 3
	2021-05-15
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	90 页码:148-158
摘要	The paper studies an Allen-Cahn-type equation defined on a time-dependent surface as a model of phase separation with order-disorder transition in a thin material layer. By a formal inner-outer expansion, it is shown that the limiting behavior of the solution is a geodesic mean curvature type flow in reference coordinates. A geometrically unfitted finite element method, known as a trace FEM, is considered for the numerical solution of the equation. The paper provides full stability analysis and convergence analysis that accounts for interpolation errors and an approximate recovery of the geometry.
关键词	Allen-Cahn Surface PDEs Evolving surfaces Trace FEM Geodesic mean curvature flow
DOI	10.1016/j.camwa.2021.03.018
收录类别	SCI
语种	英语
资助项目	NSFC[11971469] ; National Key R&D Program of China[2018YFB0704304] ; National Key R&D Program of China[2018YFB0704300] ; NSF through the Division of Mathematical Sciences[DMS-2011444] ; NSF through the Division of Mathematical Sciences[DMS/NIGMS-1953535]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000642208500015
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58588
专题	中国科学院数学与系统科学研究院
通讯作者	Olshanskii, Maxim
作者单位	1.Univ Houston, Dept Math, Houston, TX 77204 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, LSEC,ICMSEC, Beijing 100190, Peoples R China 3.Univ Maryland, Dept Math, College Pk, MD 20742 USA
推荐引用方式 GB/T 7714	Olshanskii, Maxim,Xu, Xianmin,Yushutin, Vladimir. A finite element method for Allen-Cahn equation on deforming surface[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2021,90:148-158.
APA	Olshanskii, Maxim,Xu, Xianmin,&Yushutin, Vladimir.(2021).A finite element method for Allen-Cahn equation on deforming surface.COMPUTERS & MATHEMATICS WITH APPLICATIONS,90,148-158.
MLA	Olshanskii, Maxim,et al."A finite element method for Allen-Cahn equation on deforming surface".COMPUTERS & MATHEMATICS WITH APPLICATIONS 90(2021):148-158.