  The aim of this paper is to propose an efficient adaptive finite element
method for eigenvalue problems based on the multilevel correction scheme and
inverse power method. This method involves solving associated boundary value
problems on each adaptive partitions and very low dimensional eigenvalue
problems on some special meshes which are controlled by the proposed algorithm.
Since we Hence the efficiency of solving eigenvalue problems can be improved to
be similar to the adaptive finite element method for the associated boundary
value problems. The convergence and optimal complexity is theoretically
verified and numerically demonstrated.
