  We compare the performance of two alternative algorithms which aim to
construct a force-free magnetic field given suitable boundary conditions. For
this comparison, we have implemented both algorithms on the same finite element
grid which uses Whitney forms to describe the fields within the grid cells. The
additional use of conjugate gradient and multigrid iterations result in quite
effective codes. The Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithms
both perform well for the reconstruction of a known analytic force-free field.
For more arbitrary boundary conditions the Wheatland-Sturrock-Roumeliotis
approach has some difficulties because it requires overdetermined boundary
information which may include inconsistencies. The Grad-Rubin code on the other
hand loses convergence for strong current densities. For the example we have
investigated, however, the maximum possible current density seems to be not far
from the limit beyond which a force free field cannot exist anymore for a given
normal magnetic field intensity on the boundary.
