Geodesic
Theoretical and numerical study of a free boundary problem by boundary integral methods
Crouzeix, Michel1 ; Féat, Philippe ; Sayas, Francisco-Javier2 
1 Université de Rennes 1 IRMAR, UMR 6625 Campus de Beaulieu 35042 Rennes Cedex FRANCE
2 Dep. Matemática Aplicada, Universidad de Zaragoza, Centro Politécnico Superior, c/ María de Luna, 3–50015 Zaragoza, Spain.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 6, pp. 1137-1158

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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.

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.

Classification : 35R35, 41A15, 42A12, 45G05, 65R20
Keywords: free boundary, spline, trigonometric polynomial

Crouzeix, Michel 1 ; Féat, Philippe  ; Sayas, Francisco-Javier 2

1 Université de Rennes 1 IRMAR, UMR 6625 Campus de Beaulieu 35042 Rennes Cedex FRANCE
2 Dep. Matemática Aplicada, Universidad de Zaragoza, Centro Politécnico Superior, c/ María de Luna, 3–50015 Zaragoza, Spain. 
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Crouzeix, Michel; Féat, Philippe; Sayas, Francisco-Javier. Theoretical and numerical study of a free boundary problem by boundary integral methods. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 6, pp. 1137-1158. http://geodesic.mathdoc.fr/item/M2AN_2001__35_6_1137_0/