A two-grid discretization technique is presented for solving linear eigenvalue problems posed in variational form,
Here, denotes a real Hilbert space, and and are symmetric and positive bilinear forms such that the problem exhibits a point spectrum . Two linear finite element subspaces are introduced which are defined on a coarse grid and a refined grid , respectively. Given on the coarse grid an approximate eigensolution , , then , is defined by for all together with . Asymptotic error estimates in terms of and are presented. The technique is illustrated by simple numerical experiments for the first Laplace eigenvalue problem on the unit square.