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Asymptotic modelling of conductive thin sheets

Schmidt, Kersten and Tordeux, Sébastien :
Asymptotic modelling of conductive thin sheets.
In: Z. Angew. Math. Phys., 61 (4) pp. 603-626.
[Article] , (2010)

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
Erschienen: 2010
Creators: Schmidt, Kersten and Tordeux, Sébastien
Title: Asymptotic modelling of conductive thin sheets
Language: English
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.

Journal or Publication Title: Z. Angew. Math. Phys.
Volume: 61
Number: 4
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 19 Nov 2018 21:49
DOI: 10.1007/s00033-009-0043-x
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