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A Two-dimensional eddy current model using thin inductors

Youcef Amirat·Rachid Touzani
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Abstract

We derive a mathematical model for eddy currents in two dimensional geometries where the conductors are thin domains. We assume that the current flows in the $x\_3$-direction and the inductors are domains with small diameters of order $O(ε)$. The model is derived by taking the limit $ε\to 0$. A convergence rate of $O(ε^α)$ with $0<α<1/2$ in the $L^2$--norm is shown as well as weak convergence in the $W^{1,p}$ spaces for $1< p <2$.

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Youcef Amirat, Rachid Touzani. 2006-07-11. A Two-dimensional eddy current model using thin inductors. https://arxiv.org/abs/math/0607257

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