New expansions of numerical eigenvalues by finite elements

doi:10.1016/j.cam.2007.06.011

	New expansions of numerical eigenvalues by finite elements
	Huang, Hung-Tsai ; Li, Zi-Cai 1,2; Lin, Qun3
	2008-07-15
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	217 期号:1 页码:9-27
摘要	The paper provides new expansions of leading eigenvalues for -Delta u = lambda rho u in S with the Dirichlet boundary condition u = 0 on partial derivative S by finite elements, with the support of numerical experiments. The theoretical proof of new expansions of leading eigenvalues is given only for the bilinear element Q(1). However, such a new proof technique can be applied to other elements, conforming and nonconforming. The new error expansions are reported for the Q(1) elements and other three nonconforming elements, the rotated bilinear element (denoted by Q(1)(rot)), the extension of Q(1)(rot) (denoted by E Q(1)(rot)) and Wilson's element. The expansions. imply that Q I and Q(1)(rot) yield upper bounds of the eigenvalues, and that E Q(1)(rot) and Wilson's elements yield lower bounds of the eigenvalues. By the extrapolation, the O(h(4)) convergence rate can be obtained, where h is the boundary length of uniform rectangles. (c) 2007 Elsevier B.V. All rights reserved.
关键词	bilinear elements rotated bilinear element the extension of rotated bilinear element Wilson's element Eigenvalue problem extrapolation global superconvergence
DOI	10.1016/j.cam.2007.06.011
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000256816500002
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6019
专题	计算数学与科学工程计算研究所
通讯作者	Li, Zi-Cai
作者单位	1.Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan 2.Natl Sun Yat Sen Univ, Dept Comp Sci & Engn, Kaohsiung 80424, Taiwan 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 1000080, Peoples R China
推荐引用方式 GB/T 7714	Huang, Hung-Tsai,Li, Zi-Cai,Lin, Qun. New expansions of numerical eigenvalues by finite elements[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2008,217(1):9-27.
APA	Huang, Hung-Tsai,Li, Zi-Cai,&Lin, Qun.(2008).New expansions of numerical eigenvalues by finite elements.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,217(1),9-27.
MLA	Huang, Hung-Tsai,et al."New expansions of numerical eigenvalues by finite elements".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 217.1(2008):9-27.