We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses ε are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t. to the small parameter ε and obtain optimal bound for the modelling error outside the sheet of order ${\epsilon}^{N+1}$ for the condition of order N. We end the paper with numerical experiments involving high order finite elements for sheets with varying curvature.

Classification: 65N30, 35C20, 35J25, 41A60, 35B40, 78M30, 78M35

Keywords: asymptotic expansions, transmission condition, thin conducting sheets

@article{M2AN_2011__45_6_1115_0, author = {Schmidt, Kersten and Tordeux, S\'ebastien}, title = {High order transmission conditions for thin conductive sheets in magneto-quasistatics}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, publisher = {EDP-Sciences}, volume = {45}, number = {6}, year = {2011}, pages = {1115-1140}, doi = {10.1051/m2an/2011009}, zbl = {1273.78029}, mrnumber = {2833175}, language = {en}, url = {http://www.numdam.org/item/M2AN_2011__45_6_1115_0} }

Schmidt, Kersten; Tordeux, Sébastien. High order transmission conditions for thin conductive sheets in magneto-quasistatics. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 6, pp. 1115-1140. doi : 10.1051/m2an/2011009. http://www.numdam.org/item/M2AN_2011__45_6_1115_0/

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