# 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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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 49 REFERENCES

## Variational theories for liquid crystals

VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

## Existence of minimal energy configurations of nematic liquid crystals with variable degree of orientation

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## Order reconstruction patterns in nematic liquid crystal wells

• Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• 2014
VIEW 1 EXCERPT

VIEW 1 EXCERPT

## Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids

• J. Comput. Physics
• 2013
VIEW 1 EXCERPT

## Algebraic analysis of aggregation-based multigrid

• Numerical Lin. Alg. with Applic.
• 2011
VIEW 2 EXCERPTS

VIEW 1 EXCERPT

VIEW 1 EXCERPT

VIEW 1 EXCERPT

VIEW 1 EXCERPT