Constraint-Preserving Energy-Stable Scheme for the 2D Simplified Ericksen-Leslie System (Journal of Computational Mathematics, 2021)
Here we consider the numerical approximations of the 2D simplified Ericksen-Lesliesystem. We first rewrite the system and get a new system. For the new system, we proposean easy-to-implement time discretization scheme which preserves the sphere constraint ateach node, enjoys a discrete energy law, and leads to linear and decoupled elliptic equationsto be solved at each time step. A discrete maximum principle of the scheme in the finiteelement form is also proved. Some numerical simulations are performed to validate thescheme and simulate the dynamic motion of liquid crystals.
Keywords: Nematic liquid crystal; Ericksen-Leslie system; Constraint preserving; Finite element.