A CONVERGENT ADAPTIVE FINITE ELEMENT METHOD WITH OPTIMAL COMPLEXITY

	A CONVERGENT ADAPTIVE FINITE ELEMENT METHOD WITH OPTIMAL COMPLEXITY
	Becker, Roland 1; Mao, Shipeng2 ; Shi, Zhong-Ci2
	2008
发表期刊	ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
ISSN	1068-9613
卷号	30 页码:291-304
摘要	In this paper, we introduce and analyze a simple adaptive finite element method for second order elliptic partial differential equations. The marking strategy depends on whether the data oscillation is sufficiently small compared to the error estimator in the current mesh. If the oscillation is small compared to the error estimator, we mark as many edges such that their contributions to the local estimator are at least a fixed proportion of the global error estimator (bulk criterion for the estimator). Otherwise, we reduce the oscillation by marking sufficiently many elements, such that the oscillations of the marked cells are at least a fixed proportion of the global oscillation (bulk criterion for the oscillation). This marking strategy guarantees a strict reduction of the error augmented by the oscillation term. Both convergence rates and optimal complexity of the adaptive finite element method are established, with an explicit expression of the constants in the estimates.
关键词	adaptive finite element method a posteriori error estimator convergence rate optimal computational complexity
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000267828900018
出版者	KENT STATE UNIVERSITY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6346
专题	计算数学与科学工程计算研究所
通讯作者	Becker, Roland
作者单位	1.Univ Pau, CNRS, UMR 5142, Lab Math Appl, F-64013 Pau, France 2.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Becker, Roland,Mao, Shipeng,Shi, Zhong-Ci. A CONVERGENT ADAPTIVE FINITE ELEMENT METHOD WITH OPTIMAL COMPLEXITY[J]. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS,2008,30:291-304.
APA	Becker, Roland,Mao, Shipeng,&Shi, Zhong-Ci.(2008).A CONVERGENT ADAPTIVE FINITE ELEMENT METHOD WITH OPTIMAL COMPLEXITY.ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS,30,291-304.
MLA	Becker, Roland,et al."A CONVERGENT ADAPTIVE FINITE ELEMENT METHOD WITH OPTIMAL COMPLEXITY".ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 30(2008):291-304.