RATE OF CONVERGENCE ESTIMATES FOR THE SPECTRAL
         APPROXIMATION OF A GENERALIZED EIGENVALUE PROBLEM
    

                             by


                        Carlos CONCA
            Departamento de Ingenieria Matematica 
            Fac. de Cs. Fis. y Mat., Universidad  de Chile, 
            Casilla 170/3, Correo 3, Santiago, Chile.

                        Mario DURAN
            Fac. de Matematicas, Universidad Catolica de Chile, 
            Casilla 306, Santiago 22, Chile and CMAP  
            Ecole Polytechnique, 91128 Palaiseau, France.

                        Jacques RAPPAZ
            Departement de Mathematiques, Ecole Polytechnique Federale 
            de Lausanne, 1015 Lausanne, Switzerland.
    



      The aim of this work is to derive rate of convergence estimates for the 
spectral approximation of a mathematical model, which describes the vibrations of 
a solid-fluid type structure. First, we summarize the main theoretical results and 
the discretization of this variational eigenvalue problem. Then, we state some 
well known abstract theorems on spectral approximation and apply them to our 
specific problem, which allow us to obtain the desired spectral convergence. 
Under classical regularity assumptions, we are able to establish estimates 
for the rate of convergence of the approximated eigenvalues and the gap between 
generalized eigenspaces.


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