  The magneto-frictional method is used in solar physics to compute both static
and quasi-static models of the Sun's coronal magnetic field. Here, we examine
how accurately magneto-friction (without fluid pressure) is able to predict the
relaxed state in a one-dimensional test case containing two magnetic null
points. Firstly, we show that relaxation under the full ideal
magnetohydrodynamic equations in the presence of nulls leads necessarily to a
non-force-free state, which could not be reached exactly by magneto-friction.
Secondly, the magneto-frictional solutions are shown to lead to breakdown of
magnetic flux conservation, whether or not the friction coefficient is scaled
with magnetic field strength. When this coefficient is constant, flux is
initially conserved, but only until discontinuous current sheets form at the
null points. In the ensuing weak solution, we show that magnetic flux is
dissipated at these current sheets. The breakdown of flux conservation does not
occur for an alternative viscous relaxation scheme.
