The authors consider the symmetric elliptic variational eigenvalue problem
and or . The problem is discretized using conforming and nonconforming finite elements.
The two-grid discretization scheme is given by
where the indices and refer to a coarse grid and a fine grid , respectively, and the bilinear form denotes the elementwise evaluated bilinear form .
Based on results from the abstract discretization theory of eigenvalue problems the authors prove error estimates corresponding to the approximation properties of the trial space. Numerical examples are provided for being a square or an -shaped region.