[Résultats de stabilité de lʼapproximation de deux équations des ondes faiblement couplées]
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).
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).
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@article{CRMATH_2012__350_1-2_29_0,
author = {Abdallah, Farah and Nicaise, Serge and Valein, Julie and Wehbe, Ali},
title = {Stability results for the approximation of weakly coupled wave equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {29--34},
publisher = {Elsevier},
volume = {350},
number = {1-2},
year = {2012},
doi = {10.1016/j.crma.2011.12.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.12.004/}
}
TY - JOUR AU - Abdallah, Farah AU - Nicaise, Serge AU - Valein, Julie AU - Wehbe, Ali TI - Stability results for the approximation of weakly coupled wave equations JO - Comptes Rendus. Mathématique PY - 2012 SP - 29 EP - 34 VL - 350 IS - 1-2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.12.004/ DO - 10.1016/j.crma.2011.12.004 LA - en ID - CRMATH_2012__350_1-2_29_0 ER -
%0 Journal Article %A Abdallah, Farah %A Nicaise, Serge %A Valein, Julie %A Wehbe, Ali %T Stability results for the approximation of weakly coupled wave equations %J Comptes Rendus. Mathématique %D 2012 %P 29-34 %V 350 %N 1-2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.12.004/ %R 10.1016/j.crma.2011.12.004 %G en %F CRMATH_2012__350_1-2_29_0
Abdallah, Farah; Nicaise, Serge; Valein, Julie; Wehbe, Ali. Stability results for the approximation of weakly coupled wave equations. Comptes Rendus. Mathématique, Tome 350 (2012) no. 1-2, pp. 29-34. doi : 10.1016/j.crma.2011.12.004. http://www.numdam.org/articles/10.1016/j.crma.2011.12.004/
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