Eigenvalue Approximation by Mixed and Hybrid Methods

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. 1. Introduction. The use of mixed and hybrid methods for the approximate solution of source problems has received considerable attention. We mention the works of Herrmann [20], [21], Glowinski [19], Miyoshi [29], Oden [33], Johnson [25], Mercier [27], Ciarlet-Raviart [10], Brezzi [6], [7], Scholz [42], [43], Brezzi-Raviart [8], Oden-Reddy [35], Raviart-Thomas [40], [41], Falk [14], Falk-Osborn [15], Rannacher [39], and Babuska-Osborn-Pitkranta [5]. Nemat-Nasser [30], [31],