  We study the influence of numerical methods and grid resolution on the
termination of the magnetorotational instability (MRI) by means of parasitic
instabilities in three-dimensional shearing-disc simulations reproducing
typical conditions found in core-collapse supernovae. Whether or not the MRI is
able to amplify weak magnetic fields in this context strongly depends, among
other factors, on the amplitude at which its growth terminates. The qualitative
results of our study do not depend on the numerical scheme. In all our models,
MRI termination is caused by Kelvin-Helmholtz instabilities, consistent with
theoretical predictions. Quantitatively, however, there are differences, but
numerical convergence can be achieved even at relatively low grid resolutions
if high-order reconstruction methods are used.
