QUASI-OPTIMALITY OF ADAPTIVE NONCONFORMING FINITE ELEMENT METHODS FOR THE STOKES EQUATIONS

doi:10.1137/100802967

	QUASI-OPTIMALITY OF ADAPTIVE NONCONFORMING FINITE ELEMENT METHODS FOR THE STOKES EQUATIONS
	Becker, Roland 1,2; Mao, Shipeng2,3
	2011
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	49 期号:3 页码:970-991
摘要	We prove convergence and quasi-optimal complexity of adaptive nonconforming low-order finite element methods for the Stokes equations, covering the Crouzeix-Raviart discretization on triangular and tetrahedral meshes, as well as the Rannacher-Turek discretization on two-and three-dimensional rectangular meshes. Hanging nodes are allowed in order to ease local mesh refinement. The adaptive algorithm is based on standard a posteriori error estimators consisting of two parts: a volume residual and an edge term measuring the nonconformity of the velocity approximation. We use an adaptive marking strategies, which, in each step of the iteration, takes only the dominant term into account. This paper can be regarded as an extension of [R. Becker, S. Mao, and Z.-C. Shi, SIAM J. Numer. Anal., 47 (2010), pp. 4639-4659] to the Stokes problem, but the analysis here does not make use of any relationship between mixed and nonconforming finite element methods.
关键词	adaptive finite element methods Stokes equations nonconforming finite element methods convergence optimality
DOI	10.1137/100802967
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000292033100003
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12950
专题	计算数学与科学工程计算研究所
通讯作者	Becker, Roland
作者单位	1.Univ Pau, Lab Math Appl, F-64013 Pau, France 2.Univ Pau, INRIA Bordeaux Sud Ouest Concha, F-64013 Pau, France 3.Chinese Acad Sci, AMSS, Inst Computat Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Becker, Roland,Mao, Shipeng. QUASI-OPTIMALITY OF ADAPTIVE NONCONFORMING FINITE ELEMENT METHODS FOR THE STOKES EQUATIONS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2011,49(3):970-991.
APA	Becker, Roland,&Mao, Shipeng.(2011).QUASI-OPTIMALITY OF ADAPTIVE NONCONFORMING FINITE ELEMENT METHODS FOR THE STOKES EQUATIONS.SIAM JOURNAL ON NUMERICAL ANALYSIS,49(3),970-991.
MLA	Becker, Roland,et al."QUASI-OPTIMALITY OF ADAPTIVE NONCONFORMING FINITE ELEMENT METHODS FOR THE STOKES EQUATIONS".SIAM JOURNAL ON NUMERICAL ANALYSIS 49.3(2011):970-991.