Asymptotic modelling of conductive thin sheets - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Zeitschrift für Angewandte Mathematik und Physik Year : 2010

Asymptotic modelling of conductive thin sheets


We derive and analyse models which reduce conducting sheets of a small thickness ε 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 ε, which leads to a nontrivial limit solution for ε → 0. 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(ε^{N+1}) in the exterior of the sheet and by O(ε^{N+1/2}) in its interior. We explicitly specify the models of order zero, one and two. Numerical experiments for sheets with varying curvature validate the theoretical results.
Fichier principal
Vignette du fichier
SchmidtTordeux2010.pdf (3.44 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00527608 , version 1 (13-12-2019)



Kersten Schmidt, Sébastien Tordeux. Asymptotic modelling of conductive thin sheets. Zeitschrift für Angewandte Mathematik und Physik, 2010, 61 (4), pp.603-626. ⟨10.1007/s00033-009-0043-x⟩. ⟨inria-00527608⟩
151 View
91 Download



Gmail Facebook X LinkedIn More