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A multilevel correction scheme is proposed to solve defective and nodefectiveof nonsymmetric partial differential operators by the finite element method.The method includes multi correction steps in a sequence of finite elementspaces. In each correction step, we only need to solve two source problems on afiner finite element space and two eigenvalue problems on the coarsest finiteelement space. The accuracy of the eigenpair approximation is improved aftereach correction step. This correction scheme improves overall efficiency of thefinite element method in solving nonsymmetric eigenvalue problems.

A Multilevel Correction Scheme for Nonsymmetric Eigenvalue Problems by Finite Element Methods