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Volume 3, Issue 4
Adaptive Finite Element Approximations for a Class of Nonlinear Eigenvalue Problems in Quantum Physics

Huajie Chen, Xingao Gong, Lianhua He & Aihui Zhou

DOI: 10.4208/aamm.10-m1057

Adv. Appl. Math. Mech., 3 (2011), pp. 493-518.

Published online: 2011-03

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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

Adaptive finite element, convergence, micro-structure, nonlinear eigenvalue.

  • AMS Subject Headings

35Q55, 65N15, 65N25, 65N30, 81Q05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

azhou@lsec.cc.ac.cn (Aihui Zhou)

  • BibTex
  • RIS
  • TXT
@Article{AAMM-3-493, author = {Chen , HuajieGong , XingaoHe , Lianhua and Zhou , Aihui}, title = {Adaptive Finite Element Approximations for a Class of Nonlinear Eigenvalue Problems in Quantum Physics}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2011}, volume = {3}, number = {4}, pages = {493--518}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1057}, url = {http://global-sci.org/intro/article_detail/aamm/180.html} }
TY - JOUR T1 - Adaptive Finite Element Approximations for a Class of Nonlinear Eigenvalue Problems in Quantum Physics AU - Chen , Huajie AU - Gong , Xingao AU - He , Lianhua AU - Zhou , Aihui JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 493 EP - 518 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.10-m1057 UR - https://global-sci.org/intro/article_detail/aamm/180.html KW - Adaptive finite element, convergence, micro-structure, nonlinear eigenvalue. AB -

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.

Chen , HuajieGong , XingaoHe , Lianhua and Zhou , Aihui. (2011). Adaptive Finite Element Approximations for a Class of Nonlinear Eigenvalue Problems in Quantum Physics. Advances in Applied Mathematics and Mechanics. 3 (4). 493-518. doi:10.4208/aamm.10-m1057
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