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Asymptotic Expansion of Steady-State Potential in a High Contrast Medium with a Thin Resistive Layer

Ronan Perrussel 1 Clair Poignard 2, 3 
1 LAPLACE-GRE - Groupe de Recherche en Electromagnétisme
LAPLACE - LAboratoire PLasma et Conversion d'Energie
2 MC2 - Modélisation, contrôle et calcul
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : We study the steady-state potential in a high contrast medium with a resistive thin layer. We provide asymptotic expansion of the potential at any order. Transmission conditions at any order and the corresponding variational formulation are given. We prove uniform estimates with respect to the thickness of the layer and with respect to its resistivity. The main insight consists in the uniform variational formulation whatever small the layer conductivity is. Numerical simulations illustrate the theoretical results.
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Submitted on : Tuesday, June 7, 2011 - 4:47:39 PM
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Ronan Perrussel, Clair Poignard. Asymptotic Expansion of Steady-State Potential in a High Contrast Medium with a Thin Resistive Layer. Applied Mathematics and Computation, Elsevier, 2013, 221, pp.48-65. ⟨10.1016/j.amc.2013.06.047⟩. ⟨inria-00442659v2⟩

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