TY - JOUR
T1 - Constraint-Preserving Energy-Stable Scheme for the 2D Simplified Ericksen-Leslie System
AU - Bao , Xuelian
AU - Chen , Rui
AU - Zhang , Hui
JO - Journal of Computational Mathematics
VL - 1
SP - 1
EP - 21
PY - 2020
DA - 2020/09
SN - 39
DO - http://doi.org/10.4208/jcm.1906-m2018-0144
UR - https://global-sci.org/intro/article_detail/jcm/18275.html
KW - Nematic liquid crystal, Ericksen-Leslie system, Constraint preserving, Finite element.
AB - <p style="text-align: justify;">Here we consider the numerical approximations of the 2D simplified Ericksen-Leslie
system. We first rewrite the system and get a new system. For the new system, we propose
an easy-to-implement time discretization scheme which preserves the sphere constraint at
each node, enjoys a discrete energy law, and leads to linear and decoupled elliptic equations
to be solved at each time step. A discrete maximum principle of the scheme in the finite
element form is also proved. Some numerical simulations are performed to validate the
scheme and simulate the dynamic motion of liquid crystals.</p>