A Convergent Finite Difference Scheme for the Variational Heat Equation
Numerical Analysis
2017-10-25 v1 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.1701.01265,
title = {A Convergent Finite Difference Scheme for the Variational Heat Equation},
author = {G. M. Coclite and J. Ridder and N. H. Risebro},
journal= {arXiv preprint arXiv:1701.01265},
year = {2017}
}