Comptes Rendus
no. 13-14
Partial Differential Equations/Numerical Analysis
Parallel Schwarz waveform relaxation method for a semilinear heat equation in a cylindrical domain
[Méthode de Schwarz pour l'équation de la chaleur non linéaire dans un domaine cylindrique]

Présenté par : Pierre-Louis Lions

Minh-Binh Tran1
1 LAGA, UMR 7539 of CNRS, institut Galilée, université Paris XIII, 93430 Villetaneuse, France
Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 795-799.

Nous proposons dans cette Note une preuve d'existence et de convergence de l'algorithme de Schwarz pour l'équation de la chaleur non linéaire dans un domaine cylindrique. Cette preuve repose sur l'utilisation du théorème de Banach dans un espace bien choisi, et sur de nouvelles estimations d'erreur cylindriques.

We present here a proof of well-posedness and convergence for the parallel Schwarz waveform relaxation algorithm adapted to the semilinear heat equation in a cylindrical domain. It relies on a careful estimate of a local time of existence thanks to the Banach theorem in a well chosen metric space, together with new cylindrical error estimates.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.06.004

Minh-Binh Tran 1

1 LAGA, UMR 7539 of CNRS, institut Galilée, université Paris XIII, 93430 Villetaneuse, France 
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Minh-Binh Tran. Parallel Schwarz waveform relaxation method for a semilinear heat equation in a cylindrical domain. Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 795-799. doi : 10.1016/j.crma.2010.06.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.06.004/

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