DAUGE, Monique; DULAR, Patrick; KRÄHENBÜHL, Laurent; PÉRON, Victor; PERRUSSEL, Ronan; POIGNARD, Clair

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DAUGE, Monique
Institut de Recherche Mathématique de Rennes [IRMAR]

DULAR, Patrick
Applied and Computational Electromagnetics [Liège] [ACE]

KRÄHENBÜHL, Laurent
Ampère [AMPERE]

Langue

Communication dans un congrès

Ce document a été publié dans

JSA 2013 - Journées Singulières Augmentées, 2013-08-26, Rennes. 2013

Résumé en anglais

We describe the magnetic potential in the vicinity of a corner of a conducting body embedded in a dielectric medium in a bidimensional setting. We make explicit the corner asymptotic expansion for this potential as the distance to the corner goes to zero. This expansion involves singular functions and singular coefficients. We introduce a method for the calculation of the singular functions near the corner. We extend the quasi-dual function method to the case of resonances to compute the singular coefficients. Estimates for the convergence of this method are proven. We illustrate the theoretical results with finite element computations. The specific non-standard feature of this problem lies in the structure of its singular functions: They have the form of series whose first terms are harmonic polynomials and further terms are genuine non-smooth functions generated by the piecewise constant zeroth order term of the operator.< Réduire

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251