Comptes Rendus
Partial Differential Equations
Stability results for the approximation of weakly coupled wave equations
Comptes Rendus. Mathématique, Volume 350 (2012) no. 1-2, pp. 29-34.

In this Note, we consider the approximation of two coupled wave equations with internal damping. Our goal is to damp the spurious high frequency modes by introducing numerical viscosity terms in the approximation scheme. With these viscosity terms, we show the exponential or polynomial decay of the discrete scheme when the continuous problem has such a decay (since the spectrum of the spatial operator associated with the undamped system satisfies the generalized gap condition).

Dans cette Note, nous considérons lʼapproximation de deux équations des ondes couplées avec dissipation interne. Notre but est dʼamortir les modes étranges en introduisant des termes de viscosité numérique. Avec ces termes de viscosité, nous montrons la décroissance exponentielle ou polynomiale du schéma discret lorsque le problème continu a une telle décroissance (puisque le spectre de lʼopérateur spatial associé au système sans dissipation satisfait la condition du gap généralisé).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.12.004
Farah Abdallah 1, 2; Serge Nicaise 1; Julie Valein 3; Ali Wehbe 2

1 Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, institut des sciences et techniques, 59313 Valenciennes cedex 9, France
2 Université Libanaise, faculté des sciences 1 & Hadath, Beyrouth, Liban
3 Institut Elie-Cartan Nancy (IECN), Nancy-Université & INRIA (Project-Team CORIDA), B.P. 70239, 54506 Vandoeuvre-lès-Nancy cedex, France
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Farah Abdallah; Serge Nicaise; Julie Valein; Ali Wehbe. Stability results for the approximation of weakly coupled wave equations. Comptes Rendus. Mathématique, Volume 350 (2012) no. 1-2, pp. 29-34. doi : 10.1016/j.crma.2011.12.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.12.004/

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