This book covers finite element methods for several typical eigenvalues that arise from
science and engineering. Both theory and implementation are covered in depth at the …

We present an efficient computational approach to perform real-space electronic structure
calculations using an adaptive higher-order finite-element discretization of Kohn–Sham …

In this article, we present an overview of different a posteriori error analysis and post-
processing methods proposed in the context of nonlinear eigenvalue problems, eg arising in …

A multigrid method is proposed to solve the eigenvalue problem by the finite element
method based on the combination of the multilevel correction scheme for the eigenvalue …

We propose a new normalized Sobolev gradient flow for the Gross--Pitaevskii eigenvalue
problem based on an energy inner product that depends on time through the density of the …

In this article, we provide a priori error estimates for the spectral and pseudospectral Fourier
(also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) …

This paper studies the J-method of [E. Jarlebring, S. Kvaal, W. Michiels. SIAM J. Sci. Comput.
36-4: A1978-A2001, 2014] for nonlinear eigenvector problems in a general Hilbert space …

The density functional theory (DFT) in electronic structure calculations can be formulated as
either a nonlinear eigenvalue or a direct minimization problem. The most widely used …

This work presents a new methodology for computing ground states of Bose--Einstein
condensates based on finite element discretizations on two different scales of numerical …

We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main
idea is to transform the solution of the nonlinear eigenvalue problem into a series of …