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Summary. We consider some equilibrium finite element methods for twodimensional elasticity problems. The stresses and the displacements are approximated by using piecewise linear functions. We establish Lz-estimates of order O(h 2) for both stresses and displacements.

Abstract. Rate of convergence estimates are derived for the approximation of eigenvalues and eigenvectors by mixed and hybrid methods. Several closely related abstract results on spectral approximation are proved. These results are then applied to a variety of finite element methods of mixed and hybrid type: a mixed method for 2nd order problems, mixed methods for 4th order problems, a hybrid method for 2nd order problems, and two mixed methods for the Stokes eigenvalue problem.

Rate of convergence estimates are derived for the approximation of eigenvalues and eigenvectors by mixed and hybrid methods. Several closely related abstract results on spectral approximation are proved. These results are then applied to a variety of finite element methods of mixed and hybrid type: a mixed method for 2nd order problems, mixed methods for 4th order problems, a hybrid method for 2nd order problems, and two mixed methods for the Stokes eigenvalue problem.