  Force-free magnetic fields are important in many astrophysical settings.
Determining the properties of such force-free fields -- especially smoothness
and stability properties -- is crucial to understanding many key phenomena in
astrophysical plasmas, for example energy release processes that heat the
plasma and lead to dynamic or explosive events. Here we report on a serious
limitation on the computation of force-free fields that has the potential to
invalidate the results produced by numerical force-free field solvers even for
cases in which they appear to converge (at fixed grid resolution) to an
equilibrium magnetic field. In the present work we discuss this problem within
the context of a Lagrangian relaxation scheme that conserves magnetic flux and
div(B) identically. Error estimates are introduced to assess the quality of the
calculated equilibrium. We go on to present an algorithm, based on re-writing
the curl operation via Stokes' theorem, for calculating the current which holds
great promise for improving dramatically the accuracy of the Lagrangian
relaxation procedure.
