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

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.