Convergence analysis of the adaptive finite element method with the red-green refinement

doi:10.1007/s11425-009-0200-x

	Convergence analysis of the adaptive finite element method with the red-green refinement
	Zhao XuYing3,4 ; Hu Jun 1,2; Shi ZhongCi3
	2010-02-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	53 期号:2 页码:499-512
摘要	In this paper, we analyze the convergence of the adaptive conforming P(1) element method with the red-green refinement. Since the mesh after re. ning is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).
关键词	red-green refinement adaptive finite element method convergence non-nested local refinement
DOI	10.1007/s11425-009-0200-x
语种	英语
资助项目	Natural Science Foundation of China[10601003] ; Natural Science Foundation of China[10971005] ; Foundation for the Author of National Excellent Doctoral Dissertation of China[200718] ; National Basic Research Program of China[2005CB321704]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000276596100022
出版者	SCIENCE CHINA PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10115
专题	计算数学与科学工程计算研究所
通讯作者	Hu Jun
作者单位	1.Peking Univ, Key Lab Math & Appl Math, Minist Educ, Beijing 100871, Peoples R China 2.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China 3.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Chinese Acad Sci, Grad Univ, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhao XuYing,Hu Jun,Shi ZhongCi. Convergence analysis of the adaptive finite element method with the red-green refinement[J]. SCIENCE CHINA-MATHEMATICS,2010,53(2):499-512.
APA	Zhao XuYing,Hu Jun,&Shi ZhongCi.(2010).Convergence analysis of the adaptive finite element method with the red-green refinement.SCIENCE CHINA-MATHEMATICS,53(2),499-512.
MLA	Zhao XuYing,et al."Convergence analysis of the adaptive finite element method with the red-green refinement".SCIENCE CHINA-MATHEMATICS 53.2(2010):499-512.