A finite element method for the generalized Ericksen model of nematic liquid crystals

Department of Mathematics and Center for Computation and Technology (CCT), Louisiana State University, Baton Rouge, LA 70803, USA

^* Corresponding author: walker@math.lsu.edu

Received: 7 May 2019
Accepted: 13 December 2019

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.