Eigenfunction behavior and adaptive finite element approximations of nonlinear eigenvalue problems in quantum physics

doi:10.1051/m2an/2020078

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	Eigenfunction behavior and adaptive finite element approximations of nonlinear eigenvalue problems in quantum physics
	Yang, Bin 1,2; Zhou, Aihui 1,2
	2021-02-18
发表期刊	ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
ISSN	0764-583X
卷号	55 期号:1 页码:209-227
摘要	In this paper, we investigate a class of nonlinear eigenvalue problems resulting from quantum physics. We first prove that for any open set G, there exists an eigenfunction that cannot be a polynomial on G, which may be reviewed as a refinement of the classic unique continuation property. Then we apply the non-polynomial behavior of the eigenfunction to show that the adaptive finite element approximations are convergent even if the initial mesh is not fine enough. We finally remark that similar arguments can be applied to a class of linear eigenvalue problems that improve the relevant existing results.
关键词	Adaptive finite element approximation complexity convergence nonlinear eigenvalue problem non-polynomial behavior unique continuation property
DOI	10.1051/m2an/2020078
收录类别	SCI
语种	英语
资助项目	National Key Research and Development of China[2019YFA0709601] ; Key Research Program of Frontier Sciences of the Chinese Academy of Sciences[QYZDJ-SSW-SYS010] ; National Science Foundation of China[91730302] ; National Science Foundation of China[11671389]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000619239500008
出版者	EDP SCIENCES S A
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58144
专题	中国科学院数学与系统科学研究院
通讯作者	Zhou, Aihui
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Yang, Bin,Zhou, Aihui. Eigenfunction behavior and adaptive finite element approximations of nonlinear eigenvalue problems in quantum physics[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,2021,55(1):209-227.
APA	Yang, Bin,&Zhou, Aihui.(2021).Eigenfunction behavior and adaptive finite element approximations of nonlinear eigenvalue problems in quantum physics.ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,55(1),209-227.
MLA	Yang, Bin,et al."Eigenfunction behavior and adaptive finite element approximations of nonlinear eigenvalue problems in quantum physics".ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 55.1(2021):209-227.