KMS Of Academy of mathematics and systems sciences, CAS
| A posteriori error analysis of nonconforming finite element methods for convection-diffusion problems | |
Zhang, Bei1; Chen, Shaochun1; Zhao, Jikun1; Mao, Shipeng2,3
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| 2017-09-01 | |
| Source Publication | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
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| ISSN | 0377-0427 |
| Volume | 321Pages:416-426 |
| Abstract | A unified framework is established for the a posteriori error analysis of nonconforming finite element approximations to convection-diffusion problems. Under some certain conditions, the theory assures the semi-robustness of residual error estimates in the usual energy norm and the robustness in a modified norm, and applies to several nonconforming finite elements, such as the Crouzeix-Raviart triangular element, the nonconforming rotated (NR) parallelogram element of Rannacher and Turek, the constrained NR parallelogram element, etc. Based on the general error decomposition in different norms, we show that the key ingredients of error estimation are the existence of a bounded linear operator Pi : V-h(c) -> V-h(nc) with some elementary properties and the estimation on the consistency error related to the particular numerical scheme. The numerical results are presented to illustrate the practical behavior of the error estimator and check the theoretical predictions. (C) 2017 Elsevier B.V. All rights reserved. |
| Keyword | A posteriori error estimates Semi-robustness and robustness Nonconforming quadrilateral finite elements Convection-diffusion problem |
| DOI | 10.1016/j.cam.2017.03.002 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11471329] ; National Natural Science Foundation of China[11371331] ; National Natural Science Foundation of China[11101414] ; Major State Research Development Program of China[2016YFB0201304] ; National Magnetic Confinement Fusion Science Program of China[2015GB110003] ; Youth Innovation Promotion Association of CAS[2016003] ; State Key Laboratory of Scientific and Engineering Computing (LSEC) ; National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences (NCMIS) |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000400878000028 |
| Publisher | ELSEVIER SCIENCE BV |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/25403 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Mao, Shipeng |
| Affiliation | 1.Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China 2.Chinese Acad Sci, Univ Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Univ Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Zhang, Bei,Chen, Shaochun,Zhao, Jikun,et al. A posteriori error analysis of nonconforming finite element methods for convection-diffusion problems[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2017,321:416-426. |
| APA | Zhang, Bei,Chen, Shaochun,Zhao, Jikun,&Mao, Shipeng.(2017).A posteriori error analysis of nonconforming finite element methods for convection-diffusion problems.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,321,416-426. |
| MLA | Zhang, Bei,et al."A posteriori error analysis of nonconforming finite element methods for convection-diffusion problems".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 321(2017):416-426. |
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