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 A finite element method for Allen-Cahn equation on deforming surface Olshanskii, Maxim1; Xu, Xianmin2; Yushutin, Vladimir3 2021-05-15 Source Publication COMPUTERS & MATHEMATICS WITH APPLICATIONS ISSN 0898-1221 Volume 90Pages:148-158 Abstract 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. Keyword Allen-Cahn Surface PDEs Evolving surfaces Trace FEM Geodesic mean curvature flow DOI 10.1016/j.camwa.2021.03.018 Indexed By SCI Language 英语 Funding Project 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 Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000642208500015 Publisher PERGAMON-ELSEVIER SCIENCE LTD Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/58588 Collection 中国科学院数学与系统科学研究院 Corresponding Author Olshanskii, Maxim Affiliation 1.Univ Houston, Dept Math, Houston, TX 77204 USA2.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, LSEC,ICMSEC, Beijing 100190, Peoples R China3.Univ Maryland, Dept Math, College Pk, MD 20742 USA Recommended CitationGB/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.
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