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

文献类型：期刊论文

作者Olshanskii, Maxim3; Xu, Xianmin2; Yushutin, Vladimir1
刊名COMPUTERS & MATHEMATICS WITH APPLICATIONS
出版日期2021-05-15
卷号90页码:148-158
关键词Allen-Cahn Surface PDEs Evolving surfaces Trace FEM Geodesic mean curvature flow
ISSN号0898-1221
DOI10.1016/j.camwa.2021.03.018
英文摘要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.
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
语种英语
WOS记录号WOS:000642208500015
出版者PERGAMON-ELSEVIER SCIENCE LTD
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/58587]  
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 Maryland, Dept Math, College Pk, MD 20742 USA
2.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, LSEC,ICMSEC, Beijing 100190, Peoples R China
3.Univ Houston, Dept Math, Houston, TX 77204 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.

入库方式： OAI收割

来源：数学与系统科学研究院

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