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Convergence of a standard adaptive nonconforming finite element method with optimal complexity
Mao, Shipeng1; Zhao, Xuying1,2; Shi, Zhongci1
2010-07-01
Source PublicationAPPLIED NUMERICAL MATHEMATICS
ISSN0168-9274
Volume60Issue:7Pages:673-688
AbstractIn this paper, we analyze the convergence and optimal complexity of the usual simple adaptive nonconforming finite element method by using Dorfler collective marking strategy. Based on several basic ingredients, such as the estimator reduction, quasi-orthogonality, local upper bound and so on, we eventually show the convergence of the adaptive algorithm by establishing the reduction of some total error and the quasi-optimal convergence rate. Our analysis does not need the relation between the nonconforming P(1) element and the mixed Raviart-Thomas element. The results of numerical experiments confirm that our adaptive algorithm is optimal. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
KeywordAdaptive methods Nonconforming finite elements A posteriori error estimation Convergence rate Optimal computational complexity
DOI10.1016/j.apnum.2010.03.010
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000278860100002
PublisherELSEVIER SCIENCE BV
Citation statistics
Cited Times:20[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/9319
Collection计算数学与科学工程计算研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Grad Univ, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Mao, Shipeng,Zhao, Xuying,Shi, Zhongci. Convergence of a standard adaptive nonconforming finite element method with optimal complexity[J]. APPLIED NUMERICAL MATHEMATICS,2010,60(7):673-688.
APA Mao, Shipeng,Zhao, Xuying,&Shi, Zhongci.(2010).Convergence of a standard adaptive nonconforming finite element method with optimal complexity.APPLIED NUMERICAL MATHEMATICS,60(7),673-688.
MLA Mao, Shipeng,et al."Convergence of a standard adaptive nonconforming finite element method with optimal complexity".APPLIED NUMERICAL MATHEMATICS 60.7(2010):673-688.
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