A Finite Element Method for Nematic Liquid Crystals with Variable Degree of Orientation

@article{Nochetto2017AFE,
  title={A Finite Element Method for Nematic Liquid Crystals with Variable Degree of Orientation},
  author={Ricardo H. Nochetto and Shawn W. Walker and Wujun Zhang},
  journal={SIAM J. Numerical Analysis},
  year={2017},
  volume={55},
  pages={1357-1386}
}
We consider the simplest one-constant model, put forward by J. Ericksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field $\mathbf{n}\mathbf{n}$ and its degree of orientation $s$, where the pair $(s, \mathbf{n})$ minimizes a sum of Frank-like energies and a double well potential. In particular, the Euler--Lagrange equations for the minimizer contain a degenerate elliptic equation for $\mathbf{n}$, which allows for line and… CONTINUE READING
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