Accuracy of finite element eigenproblems

The accuracy of the eigenvalues λ_r, and eigenvectors u_r of the elliptic eigenproblem of the 2mth order discretized by an arbitrary mesh of simplex finite elements has been studied. It is established as a function of r, of m, of the order of the elements and of the geometrical characteristics of the elements. Comparison with other theoretical results and with experimental results shows the present estimates to be realistic.