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abstract: 'We introduce and analyze a discontinuous Galerkin method for a time-harmonic eddy current problem formulated in terms of the magnetic field. The scheme is obtained by putting together a DG method for the approximation of the vector field variable representing the magnetic field in the conductor and a DG method for the Laplace equation whose solution is a scalar magnetic potential in the insulator. The transmission conditions linking the two problems are taken into account weakly in the global discontinuous Galerkin scheme. We prove that the numerical method is uniformly stable and obtain quasi-optimal error estimates in the DG-energy norm.'
author:
- |
    [Ana Alonso Rodríguez]{}[^1], $\,\,$ [Salim Meddahi]{}[^2]\
    and\
    [Alberto Valli]{}[^3]
title: 'A discontinuous Galerkin method for the time harmonic eddy current problem [^4]'
---

Introduction
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In this paper, we present a discontinuous Galerkin (DG) approximation of a time-harmonic eddy current problem. The eddy current approximation of Maxwell equations is obtained by disregarding the displacement current term. It is commonly used in applications related with induction heating, transformers, magnetic levitation and non-destructive testing. These problems often involve composite materials and structures, complex transmission conditions and, eventually, boundary layers due to the skin effect. The ability of 