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.