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 converge 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.
A Convergent Finite Difference Scheme for the Variational Heat Equation
COCLITE, Giuseppe Maria;
In corso di stampa
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 converge 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.File in questo prodotto:
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