GOEMHD3 simulation of the time evolution of the current density j_x at the center of a current cylinder assuming a smooth change of the resistivity. Colored lines correspond to different mesh resolutions employed for the simulations. Note that, since no analytical solution exists for this problem, the solid black line still corresponds to the analytic solution for a step-funtion-like change of the resistivity as given by Eq. (23) – as in Fig. 10.