Asymptotic modelling of conductive thin sheets

Abstract

We derive and analyse models which reduce conducting sheets of a small thickness~\eps in two dimensions to an interface and approximate their shielding behaviour by conditions on this interface. For this we consider a model problem with a conductivity scaled reciprocal to the thickness~\eps, which leads a nontrivial limit solution for~\eps\to0. The functions of the expansion are defined hierarchically, i.e. order by order. Our analysis shows that for smooth sheets the models are well defined for any order and have optimal convergence meaning that the H¹-modelling error for an expansion with ℕ~terms is bounded by~O(\epsN+1) in the exterior of the sheet and by O(\epsN+1/2) in its interior. We explicitely specify the models of order zero, one and two. Numerical experiments for sheets with varying curvature validate the theoretical results.

Item Type: Article 2010 Schmidt, Kersten and Tordeux, Sébastien Asymptotic modelling of conductive thin sheets English We derive and analyse models which reduce conducting sheets of a small thickness~\eps in two dimensions to an interface and approximate their shielding behaviour by conditions on this interface. For this we consider a model problem with a conductivity scaled reciprocal to the thickness~\eps, which leads a nontrivial limit solution for~\eps\to0. The functions of the expansion are defined hierarchically, i.e. order by order. Our analysis shows that for smooth sheets the models are well defined for any order and have optimal convergence meaning that the H¹-modelling error for an expansion with ℕ~terms is bounded by~O(\epsN+1) in the exterior of the sheet and by O(\epsN+1/2) in its interior. We explicitely specify the models of order zero, one and two. Numerical experiments for sheets with varying curvature validate the theoretical results. Z. Angew. Math. Phys. 61 4 04 Department of Mathematics04 Department of Mathematics > Numerical Analysis and Scientific Computing 19 Nov 2018 21:49 10.1007/s00033-009-0043-x EP3 XMLT2T_XMLHTML CitationBibTeXAtomEndNoteSimple MetadataJSONDublin CoreMODSReference ManagerRDF+XMLMultiline CSVASCII Citation

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