Stability and relaxation test of magnetar magnetospheres endowed with an analytic dipole field structure for different resolutions. Upper panels: total magnetospheric energy normalized to the energy of the corresponding dipole. Lower panels: time derivative of the energy normalized to the dipole. The resolutions of 16 and 32 points per stellar radius in a 3D Cartesian CARPET grid (left) correspond to the setup in Mahlmann et al. (2019). Axially symmetric simulations in spherical coordinates (right) are set up with the indicated resolution at the stellar surface. Black (solid and dashed) lines in the upper-right panel correspond to a simulation on a smaller domain, extending up to r = 935.26 M_⊙ − 6Δr, in which the pulses of the initial relaxation have sufficient time to leave the domain.