Convergence of semi-discrete approximations of Benney equations

Paulo Amorim; Mário Figueira

doi:10.1016/j.crma.2009.08.002

Partial Differential Equations/Numerical Analysis

Convergence of semi-discrete approximations of Benney equations
[Convergence d'une approximation semi-discrète des équations de Benney]

Présenté par : Gilles Lebeau

Paulo Amorim ¹ ; Mário Figueira ¹

¹ Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1135-1140.

Résumé
Abstract

Dans la première partie de cette Note, on étudie l'approximation numérique des équations de Benney dans le cas de résonance des ondes courtes et longues. On prouve la convergence d'un schéma aux différences finies semi-discret dans l'espace de l'énérgie. Dans la deuxième partie de cette Note, on condidère une version quasilinéaire des équations de Benney. On prouve la convergence d'un schéma du type Lax–Friedrichs semi-discret vers la solution d'entropie du problème.

In the first part of this Note we study the numerical approximation of Benney equations in the long wave-short wave resonance case. We prove the convergence of a finite-difference semi-discrete scheme in the energy space. In the second part of the Note we consider the semi-discretization of a quasilinear version of Benney equations. We prove the convergence of a finite-difference semi-discrete Lax–Friedrichs type scheme towards a weak entropy solution of the Cauchy problem.

Reçu le : 2009-06-17
Accepté le : 2009-08-24
Publié le : 2009-09-18

DOI : 10.1016/j.crma.2009.08.002

Affiliations des auteurs :

Paulo Amorim ¹ ; Mário Figueira ¹

¹ Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

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     author = {Paulo Amorim and M\'ario Figueira},
     title = {Convergence of semi-discrete approximations of {Benney} equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1135--1140},
     publisher = {Elsevier},
     volume = {347},
     number = {19-20},
     year = {2009},
     doi = {10.1016/j.crma.2009.08.002},
     language = {en},
}

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Paulo Amorim; Mário Figueira. Convergence of semi-discrete approximations of Benney equations. Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1135-1140. doi : 10.1016/j.crma.2009.08.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.08.002/

Bibliographie
Cité par

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