KMS Of Academy of mathematics and systems sciences, CAS
| Eigenfunction behavior and adaptive finite element approximations of nonlinear eigenvalue problems in quantum physics | |
| Yang, Bin1,2; Zhou, Aihui1,2 | |
| 2021-02-18 | |
| Source Publication | ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
 |
| ISSN | 0764-583X |
| Volume | 55Issue:1Pages:209-227 |
| Abstract | 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. |
| Keyword | Adaptive finite element approximation complexity convergence nonlinear eigenvalue problem non-polynomial behavior unique continuation property |
| DOI | 10.1051/m2an/2020078 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000619239500008 |
| Publisher | EDP SCIENCES S A |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58144 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Zhou, Aihui |
| Affiliation | 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 |
| Recommended Citation 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. |
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