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 problèmeà frontière libre intervenant en formageélectro-magnétique. Après l'avoir ramenéà un système intégro-différentiel où l'inconnue est la représentation paramétrique de la frontière, on enétudie les propriétés mathématiques essentielles. On s'intéresse ensuiteà l'approximation numérique par des méthodes de type Galerkin ou de collocation en utilisant pour l'approximation des polynômes trigonométriques ou des fonctions splines.Mathematics Subject Classification. 35R35, 41A15, 42A12, 45G05, 65R20.
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