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A posteriori error analysis of nonconforming finite element methods for convection-diffusion problems
Zhang, Bei1; Chen, Shaochun1; Zhao, Jikun1; Mao, Shipeng2,3
2017-09-01
Source PublicationJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN0377-0427
Volume321Pages:416-426
AbstractA 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.
KeywordA posteriori error estimates Semi-robustness and robustness Nonconforming quadrilateral finite elements Convection-diffusion problem
DOI10.1016/j.cam.2017.03.002
Language英语
Funding ProjectNational 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 AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000400878000028
PublisherELSEVIER SCIENCE BV
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25403
Collection计算数学与科学工程计算研究所
Corresponding AuthorMao, Shipeng
Affiliation1.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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