Stability test of magnetar magnetospheres endowed with a tilted (30 degrees) analytic dipole field structure for different resolutions. Left: evolution of the l²-norm of the error with respect to the analytical (initial) configuration normalized to the magnetic field strength B_p at the magnetar pole (top), and of the total magnetospheric energy content (bottom). Right: 3D impression of the final state (t ≈ 1.5 ms) of the intermediate resolution simulation (Δr = R_*/24). We display the magnetic field lines colorized by their norm.