Adaptive Finite Element Approximations for a Class of Nonlinear Eigenvalue Problems in Quantum Physics (Advances in Applied Mathematics and Mechanics, 2011)
In this paper, we study an adaptive finite element method for aclass of nonlinear eigenvalue problems resulting from quantumphysics that may have a nonconvex energy functional. We prove theconvergence of adaptive finite element approximations and presentseveral numerical examples of micro-structure of matter calculationsthat support our theory.