Convergence of Adaptive Finite Element Approximations for Nonlinear Eigenvalue Problems

TL;DR

This paper proves the convergence of adaptive finite element methods for nonlinear eigenvalue problems, including applications in quantum chemistry, supported by numerical examples of micro-structure calculations.

Contribution

It establishes the convergence theory for adaptive finite element approximations of nonlinear eigenvalue problems with nonconvex energy functionals.

Findings

Convergence of adaptive finite element methods is proven.

Numerical examples demonstrate micro-structure calculations.

Applications to quantum chemistry are presented.

Abstract

In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive finite element approximations and present several numerical examples of micro-structure of matter calculations that support our theory.