Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems

doi:10.1007/s00211-010-0307-6

	Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems
	Chen, Huangxin 1; Xu, Xuejun1 ; Hoppe, Ronald H. W.2,3
	2010-09-01
发表期刊	NUMERISCHE MATHEMATIK
ISSN	0029-599X
卷号	116 期号:3 页码:383-419
摘要	Recently an adaptive nonconforming finite element method (ANFEM) has been developed by Carstensen and Hoppe (in Numer Math 103:251-266, 2006). In this paper, we extend the result to some nonsymmetric and indefinite problems. The main tools in our analysis are a posteriori error estimators and a quasi-orthogonality property. In this case, we need to overcome two main difficulties: one stems from the nonconformity of the finite element space, the other is how to handle the effect of a nonsymmetric and indefinite bilinear form. An appropriate adaptive nonconforming finite element method featuring a marking strategy based on the comparison of the a posteriori error estimator and a volume term is proposed for the lowest order Crouzeix-Raviart element. It is shown that the ANFEM is a contraction for the sum of the energy error and a scaled volume term between two consecutive adaptive loops. Moreover, quasi-optimality in the sense of quasi-optimal algorithmic complexity can be shown for the ANFEM. The results of numerical experiments confirm the theoretical findings.
DOI	10.1007/s00211-010-0307-6
语种	英语
资助项目	NSF[DMS-0511624] ; NSF[DMS-0707602] ; NSF[DMS-0810176] ; NSF[DMS-0811153] ; NSF[DMS-0914788] ; National Science Foundation (NSF) of China[10731060] ; Special funds for major state basic research projects (973)[2005CB321701]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000281397600002
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10716
专题	计算数学与科学工程计算研究所
通讯作者	Chen, Huangxin
作者单位	1.Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Augsburg, Inst Math, D-86159 Augsburg, Germany 3.Univ Houston, Dept Math, Houston, TX 77204 USA
推荐引用方式 GB/T 7714	Chen, Huangxin,Xu, Xuejun,Hoppe, Ronald H. W.. Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems[J]. NUMERISCHE MATHEMATIK,2010,116(3):383-419.
APA	Chen, Huangxin,Xu, Xuejun,&Hoppe, Ronald H. W..(2010).Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems.NUMERISCHE MATHEMATIK,116(3),383-419.
MLA	Chen, Huangxin,et al."Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmetric and indefinite problems".NUMERISCHE MATHEMATIK 116.3(2010):383-419.