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

作者：Chen, Huajie; Gong, Xingao; He, Lianhua; Zhou, Aihui^*

来源：Advances in Applied Mathematics and Mechanics, 2011, 3(4): 493-518.

DOI：10.4208/aamm.10-m1057

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

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.

• 出版日期2011-8
• 单位中国科学院; 复旦大学; 中国科学院数学与系统科学研究院