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Journal Articles Applied Mathematics and Computation Year : 2013

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

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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Dates and versions

inria-00442659 , version 1 (06-01-2010)
inria-00442659 , version 2 (07-06-2011)

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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, 2013, 221, pp.48-65. ⟨10.1016/j.amc.2013.06.047⟩. ⟨inria-00442659v2⟩
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