Comptes Rendus
Coupling between scalar and vector potentials by the mortar element method
Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 933-938.

The TΩ formulation of the magnetic field is widely used in magnetodynamics. It allows the use of a scalar function in the computational domain and a vector quantity only in the conducting parts. Here we propose to approximate these two quantities on different meshes and to couple them by means of the mortar element method.

La formulation T-Ω pour le champ magnétique est largement utilisée en magnétodynamique. Elle permet d'utiliser une fonction scalaire dans tout le domaine de calcul et une quantité vectorielle seulement dans les conducteurs. On propose ici d'approcher ces deux quantités sur des maillages différents et de les coupler par la méthode des éléments avec joints.

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DOI: 10.1016/S1631-073X(02)02353-1
Yvon Maday 1; Francesca Rapetti 2; Barbara I. Wohlmuth 3

1 Laboratoire J.-L. Lions, CNRS & Université Pierre-et-Marie-Curie, boîte 187, 75252 Paris cedex 05, France
2 Laboratoire des mathématiques J.-A. Dieudonné, CNRS & Université de Nice et Sophia-Antipolis, Parc Valrose, 06108 Nice cedex 02, France
3 Universität Stuttgart, Mathematisches Institut A, Lehrstuhl 7, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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Yvon Maday; Francesca Rapetti; Barbara I. Wohlmuth. Coupling between scalar and vector potentials by the mortar element method. Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 933-938. doi : 10.1016/S1631-073X(02)02353-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02353-1/

[1] R. Albanese; G. Rubinacci Fomulation of the eddy-current problem, IEE Proc. A, Volume 137 (1990), pp. 16-22

[2] C. Bernardi; Y. Maday; A. Patera A new nonconforming approach to domain decomposition: The mortar element method (H. Brezis; J. Lions, eds.), Nonlinear Partial Differential Equations and Their Applications, Pitman, 1994, pp. 13-51

[3] Y. Maday, F. Rapetti, I.B. Wohlmuth, Mortar element coupling between global scalar and local vector potentials to solve eddy current problems, Enumath Conference Proceedings, Springer, 2002, to appear

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

[5] I.B. Wohlmuth Discretization Methods and Iterative Solvers Based on Domain Decomposition, Lecture Notes in Comput. Sci. and Engrg., 17, Springer, 2001

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