  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.
