A finite element method for the generalized Ericksen model of nematic liquid crystals
Document Type
Article
Publication Date
7-1-2020
Abstract
We consider the generalized Ericksen model of liquid crystals, which is an energy with 8 independent "elastic"constants that depends on two order parameters n (director) and s (variable degree of orientation). In addition, we present a new finite element discretization for this energy, that can handle the degenerate elliptic part without regularization, with the following properties: it is stable and it Γ-converges to the continuous energy. Moreover, it does not require the mesh to be weakly acute (which was an important assumption in our previous work). Furthermore, we include other effects such as weak anchoring (normal and tangential), as well as fully coupled electro-statics with flexo-electric and order-electric effects. We also present several simulations (in 2-D and 3-D) illustrating the effects of the different elastic constants and electric field parameters.
Publication Source (Journal or Book title)
ESAIM Mathematical Modelling and Numerical Analysis
First Page
1181
Last Page
1220
Recommended Citation
Walker, S. (2020). A finite element method for the generalized Ericksen model of nematic liquid crystals. ESAIM Mathematical Modelling and Numerical Analysis, 54 (4), 1181-1220. https://doi.org/10.1051/m2an/2019092