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Singularities of eddy current problems

Published online by Cambridge University Press:  15 November 2003

Martin Costabel ,
Monique Dauge  and
Serge Nicaise
Martin Costabel
Affiliation:
IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France. ,
Monique Dauge
Affiliation:
IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France. ,
Serge Nicaise
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, MACS, Le Mont Houy, 59313 Valenciennes Cedex 9, France.
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Abstract

We consider the time-harmonic eddy current problem in its electric formulationwhere the conductor is a polyhedral domain. By proving the convergencein energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of Bossavit [11].We describe the singularities of the solutions.They are related to edge and corner singularities of certain problems for the scalarLaplace operator, namely the interior Neumann problem, the exterior Dirichlet problem, and possibly, an interface problem. These singularities are the limit of the singularities of the related family of Maxwell problems.

Keywords

Eddy current problemcorner singularityedge singularity.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 5 , September 2003 , pp. 807 - 831
Copyright
© EDP Sciences, SMAI, 2003

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