*Fei Xu (Academy of Mathematics and Systems Science, Chinese Academy of Sciences) xufei@lsec.cc.ac.cn

Eigenvalue problems appear in a number of applications spread in many fields such as physics, chemistry, material, etc., and here a type of multilevel correction method for the eigenvalue problem will be introduced. The main idea is to transform the solution of eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and eigenvalue problems on the coarsest finite element space. For the boundary value problem, all kind of efficient iteration methods can serve as the linear problem solver. We will show that the computational work of this new scheme is truly optimal.