[Analyse numérique de la formulation en champ électrique d'un problème de courants de Foucault]
Dans cet article on analyse une méthode d'éléments finis pour la résolution numérique d'un problème de courants de Foucault dans un domaine conducteur borné. On utilise une formulation en champ électrique et on impose des conditions aux limites non-standard et non-locales. Les seules données sont les intensités d'entrée à travers la frontière du domaine qui sont imposées à l'aide de courbes contenues dans celle-ci. On démontre des estimations d'erreur optimales et on donne quelques indications sur l'implementation de la méthode sur ordinateur.
In this paper we analyze a finite element method for the numerical solution of an eddy current problem in a bounded conducting domain. We use a weak formulation in terms of the electric field and impose non-local non-standard boundary conditions. The unique data are the input current intensities which are imposed by means of some special curves lying on the boundary of the domain. Optimal error estimates are shown and implementation issues are discussed.
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@article{CRMATH_2003__337_5_359_0,
author = {Berm\'udez, Alfredo and Rodr{\i}́guez, Rodolfo and Salgado, Pilar},
title = {Numerical analysis of the electric field formulation of an eddy current problem},
journal = {Comptes Rendus. Math\'ematique},
pages = {359--364},
publisher = {Elsevier},
volume = {337},
number = {5},
year = {2003},
doi = {10.1016/S1631-073X(03)00363-7},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(03)00363-7/}
}
TY - JOUR AU - Bermúdez, Alfredo AU - Rodrı́guez, Rodolfo AU - Salgado, Pilar TI - Numerical analysis of the electric field formulation of an eddy current problem JO - Comptes Rendus. Mathématique PY - 2003 SP - 359 EP - 364 VL - 337 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(03)00363-7/ DO - 10.1016/S1631-073X(03)00363-7 LA - en ID - CRMATH_2003__337_5_359_0 ER -
%0 Journal Article %A Bermúdez, Alfredo %A Rodrı́guez, Rodolfo %A Salgado, Pilar %T Numerical analysis of the electric field formulation of an eddy current problem %J Comptes Rendus. Mathématique %D 2003 %P 359-364 %V 337 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(03)00363-7/ %R 10.1016/S1631-073X(03)00363-7 %G en %F CRMATH_2003__337_5_359_0
Bermúdez, Alfredo; Rodrı́guez, Rodolfo; Salgado, Pilar. Numerical analysis of the electric field formulation of an eddy current problem. Comptes Rendus. Mathématique, Tome 337 (2003) no. 5, pp. 359-364. doi : 10.1016/S1631-073X(03)00363-7. http://www.numdam.org/articles/10.1016/S1631-073X(03)00363-7/
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