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Robust a posteriori error estimates for conforming and nonconforming finite element methods for convection-diffusion problems
Zhao, Jikun1; Chen, Shaochun1; Zhang, Bei1; Mao, Shipeng2,3
2015-08-01
Source PublicationAPPLIED MATHEMATICS AND COMPUTATION
ISSN0096-3003
Volume264Pages:346-358
AbstractA posteriori error estimation is carried out within a unified framework for various conforming and nonconforming finite element methods for convection-diffusion problems. Our main contribution is finding an appropriate norm to measure the error, which incorporates a discrete energy norm, a discrete dual semi-norm of the convective derivative and jumps of the approximate solution over element faces (edges in two dimensions). The error estimator is shown to be robust with respect to the Peclet number in the sense of the modified norm. Based on a general error decomposition, we show that the key ingredient of error estimation is the estimation on the consistency error related to the particular numerical scheme, and the remaining terms can be bounded in a unified way. The numerical results are presented to illustrate the robustness and practical performance of the estimator in an adaptive refinement strategy. (C) 2015 Elsevier Inc. All rights reserved.
KeywordRobust a posteriori error estimates Conforming finite element Nonconforming finite element Convection diffusion problem
DOI10.1016/j.amc.2015.04.091
Language英语
Funding ProjectNational Natural Science Foundation of China[11371331] ; National Natural Science Foundation of China[11101414] ; National Natural Science Foundation of China[11471329] ; National Natural Science Foundation of China[91130026]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000355553000028
PublisherELSEVIER SCIENCE INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/19921
Collection计算数学与科学工程计算研究所
Corresponding AuthorZhao, Jikun
Affiliation1.Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China
2.Chinese Acad Sci, LSEC, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Inst Computat Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Zhao, Jikun,Chen, Shaochun,Zhang, Bei,et al. Robust a posteriori error estimates for conforming and nonconforming finite element methods for convection-diffusion problems[J]. APPLIED MATHEMATICS AND COMPUTATION,2015,264:346-358.
APA Zhao, Jikun,Chen, Shaochun,Zhang, Bei,&Mao, Shipeng.(2015).Robust a posteriori error estimates for conforming and nonconforming finite element methods for convection-diffusion problems.APPLIED MATHEMATICS AND COMPUTATION,264,346-358.
MLA Zhao, Jikun,et al."Robust a posteriori error estimates for conforming and nonconforming finite element methods for convection-diffusion problems".APPLIED MATHEMATICS AND COMPUTATION 264(2015):346-358.
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