Singularities of eddy current problems
IRMAR, Université de Rennes 1,
Campus de Beaulieu,
35042 Rennes Cedex,
2 Université de Valenciennes et du Hainaut Cambrésis, MACS, Le Mont Houy, 59313 Valenciennes Cedex 9, France.
We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in 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 . We describe the singularities of the solutions. They are related to edge and corner singularities of certain problems for the scalar Laplace 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.
Mathematics Subject Classification: 35B65 / 35R05 / 35Q60
Key words: Eddy current problem / corner singularity / edge singularity.
© EDP Sciences, SMAI, 2003