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.
Mots-clés : Eddy current problem, corner singularity, edge singularity
@article{M2AN_2003__37_5_807_0,
author = {Costabel, Martin and Dauge, Monique and Nicaise, Serge},
title = {Singularities of eddy current problems},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {807--831},
publisher = {EDP-Sciences},
volume = {37},
number = {5},
year = {2003},
doi = {10.1051/m2an:2003056},
mrnumber = {2020865},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2003056/}
}
TY - JOUR AU - Costabel, Martin AU - Dauge, Monique AU - Nicaise, Serge TI - Singularities of eddy current problems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 807 EP - 831 VL - 37 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2003056/ DO - 10.1051/m2an:2003056 LA - en ID - M2AN_2003__37_5_807_0 ER -
%0 Journal Article %A Costabel, Martin %A Dauge, Monique %A Nicaise, Serge %T Singularities of eddy current problems %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 807-831 %V 37 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2003056/ %R 10.1051/m2an:2003056 %G en %F M2AN_2003__37_5_807_0
Costabel, Martin; Dauge, Monique; Nicaise, Serge. Singularities of eddy current problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 5, pp. 807-831. doi : 10.1051/m2an:2003056. http://archive.numdam.org/articles/10.1051/m2an:2003056/
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