Error estimates in $L$$²$ of an ADI splitting scheme for the inhomogeneous Maxwell equations

In this paper we investigate an alternating direction implicit (ADI) time integration scheme for the Maxwell equations with currents, charges and conductivity. The main results establish that the scheme converges in $L$$²$ with order two to the solution of the Maxwell system. Moreover, the divergence conditions in the system are preserved with order one. These results are based on a detailed regularity analysis of both the Maxwell system and the discrete scheme.