Finite element approximations of nonlinear eigenvalue problems in quantum physics

doi:10.1016/j.cma.2011.02.008

	Finite element approximations of nonlinear eigenvalue problems in quantum physics
	Chen, Huajie; He, Lianhua; Zhou, Aihui
	2011
发表期刊	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN	0045-7825
卷号	200 期号:21-22 页码:1846-1865
摘要	In this paper, we study finite element approximations of a class of nonlinear eigenvalue problems arising from quantum physics. We derive both a priori and a posteriori finite element error estimates and obtain optimal convergence rates for both linear and quadratic finite element approximations. In particular, we analyze the convergence and complexity of an adaptive finite element method. In our analysis, we utilize certain relationship between the finite element eigenvalue problem and the associated finite element boundary value approximations. We also present several numerical examples in quantum physics that support our theory. (C) 2011 Elsevier B.V. All rights reserved.
关键词	Adaptive computation Convergence Complexity Density functional theory Finite element Nonlinear eigenvalue problem
DOI	10.1016/j.cma.2011.02.008
语种	英语
资助项目	Funds for Creative Research Groups of China[11021101] ; National Basic Research Program of China[2011CB309703] ; National High Technology Research and Development Program of China[2009AA01A134] ; National Science Foundation of China[10871198] ; National Science Foundation of China[10971059]
WOS研究方向	Engineering ; Mathematics ; Mechanics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000290842600008
出版者	ELSEVIER SCIENCE SA
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11578
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Aihui
作者单位	Chinese Acad Sci, LSEC, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Chen, Huajie,He, Lianhua,Zhou, Aihui. Finite element approximations of nonlinear eigenvalue problems in quantum physics[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2011,200(21-22):1846-1865.
APA	Chen, Huajie,He, Lianhua,&Zhou, Aihui.(2011).Finite element approximations of nonlinear eigenvalue problems in quantum physics.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,200(21-22),1846-1865.
MLA	Chen, Huajie,et al."Finite element approximations of nonlinear eigenvalue problems in quantum physics".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 200.21-22(2011):1846-1865.