Lorenz gauged vector potential formulations for the time-harmonic eddy-current problem with L∞-regularity of material properties

In this paper we consider some Lorenz gauged vector potential formulations of the eddy-current problem for the time-harmonic Maxwell equations with material properties having only L1-regularity. We prove that there exists a unique solution of these problems, and we show the convergence of a suitable finite element approximation scheme. Moreover, we show that some previously proposed Lorenz gauged formulations are indeed formulations in terms of the modified magnetic vector potential, for which the electric scalar potential is vanishing.