@Article{CiCP-25-155,
author = {Amanda E. Diegel and Shawn W. Walker},
title = {A Finite Element Method for a Phase Field Model of Nematic Liquid Crystal Droplets},
journal = {Communications in Computational Physics},
year = {2018},
volume = {25},
number = {1},
pages = {155--188},
abstract = {<p style="text-align: justify;">We develop a novel finite element method for a phase field model of nematic
liquid crystal droplets. The continuous model considers a free energy comprised of
three components: the Ericksen&#39;s energy for liquid crystals, the Cahn-Hilliard energy
representing the interfacial energy of the droplet, and an anisotropic weak anchoring
energy that enforces a condition such that the director field is aligned perpendicular
to the interface of the droplet. Applications of the model are for finding minimizers
of the free energy and exploring gradient flow dynamics. We present a finite element
method that utilizes a special discretization of the liquid crystal elastic energy, as well
as mass-lumping to discretize the coupling terms for the anisotropic surface tension
part. Next, we present a discrete gradient flow method and show that it is monotone
energy decreasing. Furthermore, we show that global discrete energy minimizers Γ-converge
to global minimizers of the continuous energy. We conclude with numerical
experiments illustrating different gradient flow dynamics, including droplet coalescence
and break-up.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0166},
url = {http://global-sci.org/intro/article_detail/cicp/12667.html}
}