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

doi:10.1016/j.cam.2017.03.002

	A posteriori error analysis of nonconforming finite element methods for convection-diffusion problems
	Zhang, Bei 1; Chen, Shaochun 1; Zhao, Jikun 1; Mao, Shipeng2,3
	2017-09-01
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	321 页码:416-426
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.
关键词	A posteriori error estimates Semi-robustness and robustness Nonconforming quadrilateral finite elements Convection-diffusion problem
DOI	10.1016/j.cam.2017.03.002
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000400878000028
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25403
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.