Comptes Rendus
no. 5
Numerical Analysis
Numerical analysis of the electric field formulation of an eddy current problem
[Analyse numérique de la formulation en champ électrique d'un problème de courants de Foucault]

Présenté par : Olivier Pironneau

Alfredo Bermúdez1 ; Rodolfo Rodrı́guez2 ; Pilar Salgado1
1 Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain
2 GI
Comptes Rendus. Mathématique, Volume 337 (2003) no. 5, pp. 359-364.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00363-7
Alfredo Bermúdez 1 ; Rodolfo Rodrı́guez 2 ; Pilar Salgado 1

1 Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain
2 GI 
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     author = {Alfredo Berm\'udez and Rodolfo Rodr{\i}́guez and Pilar Salgado},
     title = {Numerical analysis of the electric field formulation of an eddy current problem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {359--364},
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     volume = {337},
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     doi = {10.1016/S1631-073X(03)00363-7},
     language = {en},
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Alfredo Bermúdez; Rodolfo Rodrı́guez; Pilar Salgado. Numerical analysis of the electric field formulation of an eddy current problem. Comptes Rendus. Mathématique, Volume 337 (2003) no. 5, pp. 359-364. doi : 10.1016/S1631-073X(03)00363-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00363-7/

[1] A. Bermúdez; J. Bullón; F. Pena; P. Salgado A numerical method for transient simulation of metallurgical compound electrodes, Finite Elem. Anal. Des., Volume 39 (2003), pp. 283-299

[2] A. Bermúdez; R. Rodrı́guez; P. Salgado A finite element method with Lagrange multipliers for low-frequency harmonic Maxwell equations, SIAM J. Numer. Anal., Volume 40 (2002), pp. 1823-1848

[3] A. Bermúdez; R. Rodrı́guez; P. Salgado Modelling and numerical treatment of boundary data in an eddy currents problem, C. R. Acad. Sci. Paris, Ser. I, Volume 335 (2002), pp. 633-638

[4] A. Bermúdez, R. Rodrı́guez, P. Salgado, Numerical treatment of realistic boundary conditions for the eddy current problem in an electrode via Lagrange multipliers, Preprint DIM 2002-11, Universidad de Concepción, Chile, 2002

[5] A. Bermúdez, R. Rodrı́guez, P. Salgado, Finite element solution of the electric field formulation of eddy current problems in bounded domains, in preparation

[6] A. Bossavit Computational Electromagnetism. Variational Formulations, Complementarity, Edge Elements, Academic Press, San Diego, CA, 1998

[7] A. Bossavit Most general non-local boundary conditions for the Maxwell equation in a bounded region, COMPEL, Volume 19 (2000), pp. 239-245

[8] J.C. Nédélec Mixed finite elements in ℝ 3 , Numer. Math., Volume 35 (1980), pp. 315-341

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