Analysis of numerical errors in the simulations with different levels of perturbations ε, without sinkparticle. The legend is the same for both panels. To improve visibility, the results have been smoothed. Left: relative difference between σ_num and σ_an. Right: relative difference between the momentum in the disk and . We only calculated the momentum in the disk when the disk is not fragmented. The simulation with 10% of perturbations shows a non negligible amount of numerical errors, whereas all of the other simulations can be trusted.