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

Huajie Chen ,  Xingao Gong ,  Lianhua He and Aihui Zhou

10.4208/aamm.10-m1057

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

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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.

  • History

Published online: 2011-03

  • Keywords

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

  • AMS Subject Headings

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

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