Convergence of the models of the weak D-type ionization front. The CLOUDY simulation is shown by red, thin lines, the advective TPCI simulation by thick, blue lines. The discretization error (dotted), the convergence error (dashed), and the advection length (solid) are plotted against the iteration number of the steady-state solver in CLOUDY. The grid resolution of the TPCI simulation is indicated by the thin, black line. In both simulations the advection length is reduced to within a factor of 2 of the grid resolution in the hydrodynamic simulation part.