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 [11]. 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.
@article{M2AN_2003__37_5_807_0,
author = {Costabel, Martin and Dauge, Monique and Nicaise, Serge},
title = {Singularities of eddy current problems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {37},
year = {2003},
pages = {807-831},
doi = {10.1051/m2an:2003056},
mrnumber = {2020865},
zbl = {pre02029416},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2003__37_5_807_0}
}
Costabel, Martin; Dauge, Monique; Nicaise, Serge. Singularities of eddy current problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 37 (2003) pp. 807-831. doi : 10.1051/m2an:2003056. http://gdmltest.u-ga.fr/item/M2AN_2003__37_5_807_0/
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