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

doi:10.1051/m2an/2020078

	Eigenfunction behavior and adaptive finite element approximations of nonlinear eigenvalue problems in quantum physics
	Yang, Bin 1,2; Zhou, Aihui 1,2
刊名	ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
	2021-02-18
卷号	55 期号:1 页码:209-227
关键词	Adaptive finite element approximation complexity convergence nonlinear eigenvalue problem non-polynomial behavior unique continuation property
ISSN号	0764-583X
DOI	10.1051/m2an/2020078
英文摘要	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.
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
语种	英语
出版者	EDP SCIENCES S A
WOS记录号	WOS:000619239500008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58143]
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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, 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.