Robust Transmission Conditions of High Order for Thin Conducting Sheets in Two Dimensions

Resolving thin conducting sheets for shielding or even skin layers inside by the mesh of numerical methods like the finite-element method can be avoided using impedance transmission conditions (ITCs). Those ITCs shall provide an accurate approximation for small sheet thicknesses d, where the accuracy is best possible independent of the conductivity or the frequency being small or large-this we will call robustness. We investigate the accuracy and robustness of popular and recently developed ITCs, and propose robust ITCs, which are accurate up to O(d²).