Originalversjon
Zeitschrift für Angewandte Mathematik und Physik. 2017, 68 (6), DOI: http://dx.doi.org/10.1007/s00033-017-0871-z
Sammendrag
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 a viscosity type solution.