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Issue ESAIM: M2AN
Volume 35, Number 6, November-December 2001
Page(s) 1137 - 1158
DOI 10.1051/m2an:2001151

DOI: 10.1051/m2an:2001151


M2AN, Vol. 35, N°6, pp. 1137-1158

Theoretical and numerical study of a free boundary problem by boundary integral methods

Michel Crouzeix1, Philippe Féat2 and Francisco-Javier Sayas3

1  Institut de Recherche Mathématique de Rennes, UMR CNRS 6625, Université de Rennes 1, Campus de Beaulieu, Rennes, France. (Michel.Crouzeix@univ.rennes1.fr)
2  Institut de Recherche Mathématique de Rennes, UMR CNRS 6625, Université de Rennes 1, Campus de Beaulieu, Rennes, France. (Michel.Crouzeix@univ.rennes1.fr)Dep. Matemática Aplicada, Universidad de Zaragoza, Centro Politécnico Superior, c/ María de Luna, 350015 Zaragoza, Spain.
3  Dep. Matemática Aplicada, Universidad de Zaragoza, Centro Politécnico Superior, c/ María de Luna, 3-50015 Zaragoza, Spain.

(Received: November 30, 2000. Revised: July 7, 2001.)

Abstract
In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.

Résumé
Dans cet article on considère un problème à frontière libre intervenant en formage électromagnétique. Après l'avoir ramené à un système intégro-différentiel où l'inconnue est la représentation paramétrique de la frontière, on en étudie les propriétés mathématiques essentielles. On s'intéresse ensuite à l'approximation numérique par des méthodes de type Galerkin ou de collocation en utilisant pour l'approximation des polynômes trigonométriques ou des fonctions splines.


AMS Subject: 35R35, 41A15, 42A12, 45G05, 65R20

Key words: Free boundary, spline, trigonometric polynomial.


© EDP Sciences, SMAI 2001


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