The Multilevel Finite Element Discretizations Based on Local Defect-Correction for Nonsymmetric Eigenvalue Problems

TL;DR

This paper introduces new multilevel finite element discretizations using local defect-correction for nonsymmetric eigenvalue problems, providing efficient solutions and local error estimates that include corner points.

Contribution

It develops novel three-level and multilevel finite element schemes based on local defect-correction, extending error analysis to local domains with corner points.

Findings

Schemes are simple and easy to implement.

Numerical experiments confirm efficiency for singular nonsymmetric eigenvalue problems.

Local error estimates are applicable to domains with corner points.

Abstract

Based on the work of Xu and Zhou [Math.Comput., 69(2000), pp.881-909], we establish new three-level and multilevel finite element discretizations by local defect-correction technique. Theoretical analysis and numerical experiments show that the schemes are simple and easy to carry out, and can be used to solve singular nonsymmetric eigenvalue problems efficiently. We also discuss the local error estimates of finite element approximations; it's a new feature here that the estimates apply to the local domains containing corner points.