Convergence of a standard adaptive nonconforming finite element method with optimal complexity

doi:10.1016/j.apnum.2010.03.010

	Convergence of a standard adaptive nonconforming finite element method with optimal complexity
	Mao, Shipeng1 ; Zhao, Xuying1,2 ; Shi, Zhongci1
	2010-07-01
发表期刊	APPLIED NUMERICAL MATHEMATICS
ISSN	0168-9274
卷号	60 期号:7 页码:673-688
摘要	In 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.
关键词	Adaptive methods Nonconforming finite elements A posteriori error estimation Convergence rate Optimal computational complexity
DOI	10.1016/j.apnum.2010.03.010
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000278860100002
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9319
专题	计算数学与科学工程计算研究所
通讯作者	Zhao, Xuying
作者单位	1.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
推荐引用方式 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.