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A posteriori error analysis of nonconforming finite element methods for convection-diffusion problems

文献类型：期刊论文

作者Zhang, Bei1; Chen, Shaochun1; Zhao, Jikun1; Mao, Shipeng2,3
刊名JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
出版日期2017-09-01
卷号321页码:416-426
关键词A posteriori error estimates Semi-robustness and robustness Nonconforming quadrilateral finite elements Convection-diffusion problem
ISSN号0377-0427
DOI10.1016/j.cam.2017.03.002
英文摘要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.
资助项目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研究方向Mathematics
语种英语
WOS记录号WOS:000400878000028
出版者ELSEVIER SCIENCE BV
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/25402]  
专题计算数学与科学工程计算研究所
通讯作者Mao, Shipeng
作者单位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
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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