KMS Of Academy of mathematics and systems sciences, CAS
| 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 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 |
| Recommended Citation 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. |
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