# A Multilevel Correction Method for Steklov Eigenvalue Problem by Nonconforming Finite Element Methods

@article{Han2015AMC, title={A Multilevel Correction Method for Steklov Eigenvalue Problem by Nonconforming Finite Element Methods}, author={Xiaole Han and Yu Li and Hehu Xie}, journal={Numerical Mathematics-theory Methods and Applications}, year={2015}, volume={8}, pages={383-405} }

In this paper, a multilevel correction scheme is proposed to solve the Steklov eigenvalue problem by nonconforming finite element methods. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an Steklov eigenvalue problem on the coarsest finite element space. This correction scheme can increase the overall efficiency of solving eigenvalue problems by the…

## 16 Citations

A multigrid correction scheme for a new Steklov eigenvalue problem in inverse scattering

- Mathematics, Computer ScienceInt. J. Comput. Math.
- 2020

A multigrid correction scheme to solve a new Steklov eigenvalue problem in inverse scattering is proposed and error estimates of eigenvalues and eigenfunctions are proved.

Local defect-correction method based on multilevel discretization for Steklov eigenvalue problem

- ESAIM: Mathematical Modelling and Numerical Analysis
- 2021

In this paper, we propose a local defect-correction method for solving the Steklov eigenvalue problem arising from the scalar second order positive definite partial differential equations based on…

A full multigrid method for the Steklov eigenvalue problem

- Computer Science, MathematicsInt. J. Comput. Math.
- 2019

This paper introduces a kind of parallel multigrid method for solving Steklov eigenvalue problem based on the multilevel correction method and proves that the computational work of this new scheme is truly optimal, the same as solving the corresponding linear boundary value problem.

The adaptive finite element method for the Steklov eigenvalue problem in inverse scattering

- Mathematics
- 2020

Abstract In this study, for the first time, we discuss the posteriori error estimates and adaptive algorithm for the non-self-adjoint Steklov eigenvalue problem in inverse scattering. The…

An accurate a posteriori error estimator for the Steklov eigenvalue problem and its applications

- MathematicsScience China Mathematics
- 2019

In this paper, a type of accurate a posteriori error estimator is proposed for the Steklov eigenvalue problem based on the complementary approach, which provides an asymptotic exact estimate for the…

A Multilevel Correction Method for Interior Transmission Eigenvalue Problem

- Mathematics, Computer ScienceJ. Sci. Comput.
- 2017

A numerical analysis for the transmission eigenvalue problem by the finite element method and the proposed multilevel correction method improves the overfull efficiency of the transmission Eigenvalue solving.

Spectral Indicator Method for a Non-selfadjoint Steklov Eigenvalue Problem

- Computer Science, MathematicsJ. Sci. Comput.
- 2019

An efficient numerical method is proposed for a non-selfadjoint Steklov eigenvalue problem using the recently developed spectral indicator method to compute eigenvalues in a given region on the complex plane.

An asymptotically exact a posteriori error estimator for non-selfadjoint Steklov eigenvalue problem

- Mathematics
- 2020

Abstract This paper aims to introduce an asymptotically exact a posteriori error estimator for non-selfadjoint Steklov eigenvalue problem arising from inverse scattering by using the complementary…

Guaranteed Eigenvalue Bounds for the Steklov Eigenvalue Problem

- Mathematics, Computer ScienceSIAM J. Numer. Anal.
- 2019

An enhanced version of the eigenvalue estimation algorithm developed by the third author is proposed, which removes the requirements of the positive definiteness of bilinear forms in the formulation of eigen value problems.

Energy Error Estimates of Subspace Method and Multigrid Algorithm for Eigenvalue Problems

- Mathematics
- 2017

This paper is to give a new understanding and applications of the subspace projection method for selfadjoint eigenvalue problems. A new error estimate in the energy norm, which is induced by the…

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