Eddy currents and corner singularities

The eddy current problem is addressed in this paper, in a bidimensional setting where the conducting medium is non- magnetic and has a corner singularity. For any fixed skin depth we describe the behaviour of the potential near the corner, which is not singular at the corner, unlike the perfect conducting case. Then as δ goes to zero, the first two terms of a multiscale expansion of the potential are introduced to tackle the magneto-harmonic problem. The heuristics of the method are given and numerical computations illustrate the obtained accuracy.