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 QUASI-OPTIMALITY OF ADAPTIVE NONCONFORMING FINITE ELEMENT METHODS FOR THE STOKES EQUATIONS Becker, Roland1,2; Mao, Shipeng2,3 2011 Source Publication SIAM JOURNAL ON NUMERICAL ANALYSIS ISSN 0036-1429 Volume 49Issue:3Pages:970-991 Abstract 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. Keyword adaptive finite element methods Stokes equations nonconforming finite element methods convergence optimality DOI 10.1137/100802967 Language 英语 WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000292033100003 Publisher SIAM PUBLICATIONS Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/12950 Collection 计算数学与科学工程计算研究所 Corresponding Author Becker, Roland Affiliation 1.Univ Pau, Lab Math Appl, F-64013 Pau, France2.Univ Pau, INRIA Bordeaux Sud Ouest Concha, F-64013 Pau, France3.Chinese Acad Sci, AMSS, Inst Computat Math, Beijing 100190, Peoples R China Recommended CitationGB/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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