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OPTIMAL QUADRATIC NITSCHE EXTENDED FINITE ELEMENT METHOD FOR INTERFACE PROBLEM OF DIFFUSION EQUATION
Wang, Fei1,2; Zhang, Shuo3
2018
Source PublicationJOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN0254-9409
Volume36Issue:5Pages:693-717
AbstractIn this paper, we study Nitsche extended finite element method (XFEM) for the interface problem of a two dimensional diffusion equation. Specifically, we study the quadratic XFEM scheme on some shape-regular family of grids and prove the optimal convergence rate of the scheme with respect to the mesh size. Main efforts are devoted onto classifying the cases of intersection between the elements and the interface and prove a weighted trace inequality for the extended finite element functions needed, and the general framework of analysing XFEM can be implemented then.
KeywordInterface problems Extended finite element methods Error estimates Nitsche's scheme Quadratic element
DOI10.4208/jcm.1703-m2015-0340
Language英语
Funding ProjectU.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials[DE-SC-0009249] ; Key Program of National Natural Science Foundation of China[91430215] ; State Key Laboratory of Scientific and Engineering Computing (LSEC) ; National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences (NCMIS) ; National Natural Science Foundation of China[11471026]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000455996800005
PublisherGLOBAL SCIENCE PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32173
Collection计算数学与科学工程计算研究所
Affiliation1.Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China
2.Penn State Univ, Dept Math, University Pk, PA 16802 USA
3.Chinese Acad Sci, LSEC, ICMSEC, NCMIS,Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Wang, Fei,Zhang, Shuo. OPTIMAL QUADRATIC NITSCHE EXTENDED FINITE ELEMENT METHOD FOR INTERFACE PROBLEM OF DIFFUSION EQUATION[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2018,36(5):693-717.
APA Wang, Fei,&Zhang, Shuo.(2018).OPTIMAL QUADRATIC NITSCHE EXTENDED FINITE ELEMENT METHOD FOR INTERFACE PROBLEM OF DIFFUSION EQUATION.JOURNAL OF COMPUTATIONAL MATHEMATICS,36(5),693-717.
MLA Wang, Fei,et al."OPTIMAL QUADRATIC NITSCHE EXTENDED FINITE ELEMENT METHOD FOR INTERFACE PROBLEM OF DIFFUSION EQUATION".JOURNAL OF COMPUTATIONAL MATHEMATICS 36.5(2018):693-717.
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