  The variational heat equation is a nonlinear, parabolic equation not in
divergence form that arises as a model for the dynamics of the director field
in a nematic liquid crystal. We present a finite difference scheme for a
transformed, possibly degenerate version of this equation and prove that a
subsequence of the numerical solutions converges to a weak solution. This
result is supplemented by numerical examples that show that weak solutions are
not unique and give some intuition about how to obtain the physically relevant
solution.
