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QUASI-OPTIMALITY OF ADAPTIVE NONCONFORMING FINITE ELEMENT METHODS FOR THE STOKES EQUATIONS
Becker, Roland1,2; Mao, Shipeng2,3
2011
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume49Issue:3Pages:970-991
AbstractWe 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.
Keywordadaptive finite element methods Stokes equations nonconforming finite element methods convergence optimality
DOI10.1137/100802967
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000292033100003
PublisherSIAM PUBLICATIONS
Citation statistics
Cited Times:22[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/12950
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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