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 …

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 …

A new type of iteration method is proposed in this paper to solve the Steklov eigenvalue
problem by the finite element method. In this scheme, solving the Steklov eigenvalue …

In this paper, we analyze the convergence of a finite element method for the computation of
transmission eigenvalues and corresponding eigenfunctions. Based on the obtained error …

In topology optimization, finite element methods are usually required to solve state
equations repeatedly. Considerable computational costs are required for iterative solvers to …

In this paper, a full (nested) multigrid scheme is proposed to solve eigenvalue problems. The
idea here is to use a correction method to transform the eigenvalue problem solving to a …

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 …

A locally optimal preconditioned Newton-Schur method is proposed for solving symmetric
elliptic eigenvalue problems. Firstly, the Steklov-Poincaré operator is used to project the …

In this paper, an adaptive finite element method is proposed for solving Kohn–Sham
equation with the multilevel correction technique. In the method, the Kohn–Sham equation is …