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 …

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 …

Density functional theory (DFT) provides the most widely used models for simulating
molecules and materials based on the fundamental laws of quantum mechanics. It earned …

The Kohn--Sham model is a powerful, widely used approach for computation of ground state
electronic energies and densities in chemistry, materials science, biology, and nanoscience …

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) …

The ground states of Bose–Einstein condensates in a rotating frame can be described as
constrained minimizers of the Gross–Pitaevskii energy functional with an angular …

In this paper, we study finite element approximations of a class of nonlinear eigenvalue
problems arising from quantum physics. We derive both a priori and a posteriori finite …

This work considers the numerical computation of ground states of rotating Bose-Einstein
condensates (BECs) which can exhibit a multiscale lattice of quantized vortices. This …

An adaptive finite element method for eigenvalue problems is proposed based on the
multilevel correction scheme. Different from the standard adaptive finite element method …

In this paper, we employ the weak Galerkin (WG) finite element method and the imaginary
time method to compute both the ground state and the excited states in Bose-Einstein …