Pour les méthodes de pénalisation de domaine, il est possible qu'il y ait un écart entre la vitesse de convergence attendue et celle observée numériquement. Un tel écart a été mis en évidence par Paccou, et al. [A. Paccou, G. Chiavassa, J. Liandrat, K. Schneider, A penalization method applied to the wave equation, C. R. Mecanique 333 (2005) 79–85], lors de la pénalisation d'une équation des ondes. On répond ici à une question posée dans, en prouvant que le défaut de vitesse de convergence observé est clairement provoqué par la formation de couches limites, localisées d'un seul côté du bord.
For domain penalization methods, there can be a gap between the expected speed of convergence and the observed one, by numerical means. Such a gap has been observed by Paccou, et al. [A. Paccou, G. Chiavassa, J. Liandrat, K. Schneider, A penalization method applied to the wave equation, C. R. Mecanique 333 (2005) 79–85], concerning the penalization of a wave equation. We answer here one of their questions by proving that the observed lack in convergence speed is clearly related to the formation of boundary layers on one side of the boundary.
@article{CRMECA_2008__336_5_454_0, author = {Bruno Fornet}, title = {Influence of boundary layers over the rate of convergence in a penalization method for a {1-D} wave equation}, journal = {Comptes Rendus. M\'ecanique}, pages = {454--457}, publisher = {Elsevier}, volume = {336}, number = {5}, year = {2008}, doi = {10.1016/j.crme.2008.01.009}, language = {en}, }
TY - JOUR AU - Bruno Fornet TI - Influence of boundary layers over the rate of convergence in a penalization method for a 1-D wave equation JO - Comptes Rendus. Mécanique PY - 2008 SP - 454 EP - 457 VL - 336 IS - 5 PB - Elsevier DO - 10.1016/j.crme.2008.01.009 LA - en ID - CRMECA_2008__336_5_454_0 ER -
Bruno Fornet. Influence of boundary layers over the rate of convergence in a penalization method for a 1-D wave equation. Comptes Rendus. Mécanique, Volume 336 (2008) no. 5, pp. 454-457. doi : 10.1016/j.crme.2008.01.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.01.009/
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