Numerical solution of the Monge–Ampère equation by a Newton's algorithm

Grégoire Loeper; Francesca Rapetti

doi:10.1016/j.crma.2004.12.018

Numerical Analysis/Partial Differential Equations

Numerical solution of the Monge–Ampère equation by a Newton's algorithm
[Une méthode numérique de résolution de l'equation de Monge–Ampère]

Présenté par : Roland Glowinski

Grégoire Loeper ¹ ; Francesca Rapetti ²

¹ Département de mathématiques, École polytechnique fédérale de Lausanne, CH-1015 Lausanne, Switzerland
² Laboratoire J.-A. Dieudonné, CNRS & université de Nice et Sophia-Antipolis, parc Valrose, 06108 Nice cedex 02, France

Comptes Rendus. Mathématique, Volume 340 (2005) no. 4, pp. 319-324.

Résumé
Abstract

Nous résolvons numériquement l'équation de Monge–Ampère avec donnée au bord périodique en utilisant un algorithme de Newton. Nous prouvons la convergence de l'algorithme, et présentons quelques exemples numériques, pour lesquels une bonne approximation de la solution est obtenue en 10 itérations.

We solve numerically the Monge–Ampère equation with periodic boundary condition using a Newton's algorithm. We prove convergence of the algorithm, and present some numerical examples, for which a good approximation is obtained in 10 iterations.

Reçu le : 2004-11-16
Accepté le : 2004-12-17
Publié le : 2005-01-21

DOI : 10.1016/j.crma.2004.12.018

Affiliations des auteurs :

Grégoire Loeper ¹ ; Francesca Rapetti ²

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     author = {Gr\'egoire Loeper and Francesca Rapetti},
     title = {Numerical solution of the {Monge{\textendash}Amp\`ere} equation by a {Newton's} algorithm},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {319--324},
     publisher = {Elsevier},
     volume = {340},
     number = {4},
     year = {2005},
     doi = {10.1016/j.crma.2004.12.018},
     language = {en},
}

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Grégoire Loeper; Francesca Rapetti. Numerical solution of the Monge–Ampère equation by a Newton's algorithm. Comptes Rendus. Mathématique, Volume 340 (2005) no. 4, pp. 319-324. doi : 10.1016/j.crma.2004.12.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.12.018/

Bibliographie
Cité par

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