On the convergence of eigenvalues for mixed formulations

Eigenvalue problems for mixed formulation show peculiar features that make them substantially different from the corresponding mixed direct problems. In this paper we analyze, in an abstract framework, necessary and sufficient conditions for their convergence.

[1]  I. Babuska The finite element method with Lagrangian multipliers , 1973 .

[2]  F. Brezzi On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[3]  R. Kellogg,et al.  A regularity result for the Stokes problem in a convex polygon , 1976 .

[4]  Michel Fortin,et al.  An analysis of the convergence of mixed finite element methods , 1977 .

[5]  G. Fix Review: Philippe G. Ciarlet, The finite element method for elliptic problems , 1979 .

[6]  R. S. Falk,et al.  Error estimates for mixed methods , 1980 .

[7]  B. Mercier,et al.  Eigenvalue approximation by mixed and hybrid methods , 1981 .

[8]  Claes Johnson,et al.  Analysis of some mixed finite element methods related to reduced integration , 1982 .

[9]  J. Tinsley Oden,et al.  Stability of some mixed finite element methods for Stokesian flows , 1984 .

[10]  R. A. Nicolaides,et al.  On the stability of bilinear-constant velocity-pressure finite elements , 1984 .

[11]  L. D. Marini,et al.  Two families of mixed finite elements for second order elliptic problems , 1985 .

[12]  Jean E. Roberts,et al.  Mixed and hybrid finite element methods , 1987 .

[13]  M. Fortin,et al.  E cient rectangular mixed fi-nite elements in two and three space variables , 1987 .

[14]  K. Bathe,et al.  A mixed displacement-based finite element formulation for acoustic fluid-structure interaction , 1995 .

[15]  E. Christiansen,et al.  Handbook of Numerical Analysis , 1996 .

[16]  Klaus-Jürgen Bathe,et al.  On Mixed Elements for Acoustic Fluid-Structure Interactions , 1997 .