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Adaptive Finite Element Approximations for a Class of Nonlinear Eigenvalue Problems in Quantum Physics

Published online by Cambridge University Press:  03 June 2015

Huajie Chen ,
Xingao Gong ,
Lianhua He  and
Aihui Zhou
Huajie Chen*
Affiliation:
LSEC, Institute of Computational Mathematics and Scientific/ Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Xingao Gong*
Affiliation:
Department of Physics, Fudan University, Shanghai 200433, China
Lianhua He*
Affiliation:
LSEC, Institute of Computational Mathematics and Scientific/ Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Aihui Zhou*
Affiliation:
LSEC, Institute of Computational Mathematics and Scientific/ Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
Email: hjchen@lsec.cc.ac.cn
Email: xggong@fudan.edu.cn
Email: helh@lsec.cc.ac.cn
Corresponding author. Email: azhou@lsec.cc.ac.cn
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Abstract

In this paper, we study an adaptive finite element method for a class of nonlinear eigenvalue problems resulting from quantum physics that may have a nonconvex energy functional. We prove the convergence of adaptive finite element approximations and present several numerical examples of micro-structure of matter calculations that support our theory.

Keywords

35Q5565N1565N2565N3081Q05Adaptive finite elementconvergencemicro-structurenonlinear eigenvalue
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 4 , August 2011 , pp. 493 - 518
Copyright
Copyright © Global-Science Press 2011

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