Lorenz gauged vector potential formulations for the time-harmonic eddy-current problem with $L^\infty$-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 L-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. Copyright © 2007 John Wiley & Sons, Ltd.