Convergence of discrete Laplace-Beltrami operators over surfaces

doi:10.1016/j.camwa.2004.05.001

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	Convergence of discrete Laplace-Beltrami operators over surfaces
	Xu, GL
	2004-08-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	48 期号:3-4 页码:347-360
摘要	The convergence property of the discrete Laplace-Beltrami operator is the foundation of convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator. The aim of this paper is to review several already-used discrete Laplace-Beltrami operators over triangulated surface and study numerically, as well as theoretically, their convergent behavior. We show that none of them is convergent in general, but two of them, proposed by Desbrun et al. and Meyer et al., are convergent in a special case. We point out that this special case is very important in the numerical simulation of geometric partial differential equations. (C) 2004 Elsevier Ltd. All rights reserved.
关键词	Laplace-Beltrami operator surface triangulation convergence
DOI	10.1016/j.camwa.2004.05.001
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000224364400002
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/897
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, GL
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Xu, GL. Convergence of discrete Laplace-Beltrami operators over surfaces[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2004,48(3-4):347-360.
APA	Xu, GL.(2004).Convergence of discrete Laplace-Beltrami operators over surfaces.COMPUTERS & MATHEMATICS WITH APPLICATIONS,48(3-4),347-360.
MLA	Xu, GL."Convergence of discrete Laplace-Beltrami operators over surfaces".COMPUTERS & MATHEMATICS WITH APPLICATIONS 48.3-4(2004):347-360.