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 …

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 …

This paper discusses highly efficient discretization schemes for solving self-adjoint elliptic
differential operator eigenvalue problems. Several new two-grid discretization schemes …

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 paper discusses a high efficient scheme for the Steklov eigenvalue problem. A two-grid
discretization scheme of nonconforming Crouzeix–Raviart element is established. With this …

In the paper, a two-grid discretization scheme is discussed for the Steklov eigenvalue
problem. With the scheme, the solution of the Steklov eigenvalue problem on a fine grid is …

To introduce the finite volume method to electronic structure calculations, we study a
symmetric finite volume scheme for a class of linear eigenvalue problems and present a …

In this paper, a novel multigrid method based on Newton iteration is proposed to solve
nonlinear eigenvalue problems. Instead of handling the eigenvalue λ and eigenfunction u …

In this paper, we propose a method to improve the convergence rate of the lowest order
Raviart–Thomas mixed finite element approximations for the second order elliptic …

This paper discusses efficient numerical methods for the Steklov eigenvalue problem and
establishes a new multiscale discretization scheme and an adaptive algorithm based on the …