Error estimates for finite volume element methods for general second-order elliptic problems

doi:10.1002/num.10068

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	Error estimates for finite volume element methods for general second-order elliptic problems
	Wu, HJ ; Li, RH
	2003-11-01
发表期刊	NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0749-159X
卷号	19 期号:6 页码:693-708
摘要	We treat the finite volume element method (FVE) for solving general second order elliptic problems as a perturbation of the linear finite element method (FEM), and obtain the optimal H-1 error estimate, H-1 superconvergence and L-P (1 < p less than or equal to infinity) error estimates between the solution of the FVE and that of the FEM. In particular, the superconvergence result does not require any extra assumptions on the mesh except quasi-uniform. Thus the error estimates of the FVE can be derived by the standard error estimates of the FEM. Moreover we consider the effects of numerical integration and prove that the use of barycenter quadrature rule does not decrease the convergence orders of the FVE. The results of this article reveal that the FVE is in close relationship with the FEM. (C) 2003 Wiley Periodicals, Inc.
关键词	finite volume element method error estimates elliptic problems
DOI	10.1002/num.10068
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000186105400001
出版者	JOHN WILEY & SONS 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/19086
专题	中国科学院数学与系统科学研究院
通讯作者	Wu, HJ
作者单位	1.Jilin Univ, Coll Math, Changchun 130012, Peoples R China 2.Chinese Acad Sci, Inst Computat Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Wu, HJ,Li, RH. Error estimates for finite volume element methods for general second-order elliptic problems[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2003,19(6):693-708.
APA	Wu, HJ,&Li, RH.(2003).Error estimates for finite volume element methods for general second-order elliptic problems.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,19(6),693-708.
MLA	Wu, HJ,et al."Error estimates for finite volume element methods for general second-order elliptic problems".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 19.6(2003):693-708.