Singularities of eddy current problems

Martin Costabel; Monique Dauge; Serge Nicaise

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 5, page 807-831
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Costabel, Martin, Dauge, Monique, and Nicaise, Serge. "Singularities of eddy current problems." ESAIM: Mathematical Modelling and Numerical Analysis 37.5 (2010): 807-831. <http://eudml.org/doc/194192>.

@article{Costabel2010,
abstract = { 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. },
author = {Costabel, Martin, Dauge, Monique, Nicaise, Serge},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Eddy current problem; corner singularity; edge singularity.},
language = {eng},
month = {3},
number = {5},
pages = {807-831},
publisher = {EDP Sciences},
title = {Singularities of eddy current problems},
url = {http://eudml.org/doc/194192},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Costabel, Martin
AU - Dauge, Monique
AU - Nicaise, Serge
TI - Singularities of eddy current problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 5
SP - 807
EP - 831
AB - 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.
LA - eng
KW - Eddy current problem; corner singularity; edge singularity.
UR - http://eudml.org/doc/194192
ER -

References

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