A Trefftz Method for the Time-Harmonic Eddy Current Equation

We present a discontinuous finite element method to resolve the skin effect in conductors on coarse meshes. The idea is to take into account the exponential decay in the finite element trial space, which enables to resolve the skin layer independent of the size of the mesh cells. The discontinuous, Trefftz-type basis functions are coupled across the element boundaries by the interior penalty-/Nitsche's method and numerical experiments affirm the effectiveness of the method for thin boundary layers.