Robust a posteriori error estimates for conforming and nonconforming finite element methods for convection-diffusion problems

doi:10.1016/j.amc.2015.04.091

	Robust a posteriori error estimates for conforming and nonconforming finite element methods for convection-diffusion problems
	Zhao, Jikun 1; Chen, Shaochun 1; Zhang, Bei 1; Mao, Shipeng2,3
	2015-08-01
发表期刊	APPLIED MATHEMATICS AND COMPUTATION
ISSN	0096-3003
卷号	264 页码:346-358
摘要	A 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.
关键词	Robust a posteriori error estimates Conforming finite element Nonconforming finite element Convection diffusion problem
DOI	10.1016/j.amc.2015.04.091
语种	英语
资助项目	National 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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000355553000028
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19921
专题	计算数学与科学工程计算研究所
通讯作者	Zhao, Jikun
作者单位	1.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
推荐引用方式 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.