KMS Of Academy of mathematics and systems sciences, CAS
| QUASI-OPTIMALITY OF ADAPTIVE NONCONFORMING FINITE ELEMENT METHODS FOR THE STOKES EQUATIONS | |
Becker, Roland1,2; Mao, Shipeng2,3
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| 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, 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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