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C. Conca (1)
M. Duran (2)
J. Rappaz (3)
| (1) | Departamento de Ingenieria Matematica Fac. de Cs. Fis. y Mat., Universidad de Chile, Casilla 170/3, Correo 3, Santiago, Chile. |
| (2) | Fac. de Matematicas, Universidad Catolica de Chile, Casilla 306, Santiago 22, Chile CMAP Ecole Polytechnique, 91128 Palaiseau, France. |
| (3) | Departement de Mathematiques, Ecole Polytechnique Federale de Lausanne, 1015 Lausanne, Switzerland. |
Abstract : 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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