@article{Wang2022, 
author = {Danxia Wang and Ni Miao and Jing Liu},
title = {A second-order numerical scheme for the Ericksen-Leslie equation},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {9},
pages = {15834-15853},
keywords = {Ericksen-Leslie equation, nematic liquid crystal, finite element, second-order accuracy, pressure-correction},
url = {https://www.sciopen.com/article/10.3934/math.2022867},
doi = {10.3934/math.2022867},
abstract = {In this paper, we consider a finite element approximation for the Ericksen-Leslie model of nematic liquid crystal. Based on a saddle-point formulation of the director vector, a second-order backward differentiation formula (BDF) numerical scheme is proposed, where a pressure-correction strategy is used to decouple the computation of the pressure from that of the velocity. Designing this scheme leads to solving a linear system at each time step. Furthermore, via implementing rigorous theoretical analysis, we prove that the proposed scheme enjoys the energy dissipation law. Some numerical simulations are also performed to demonstrate the accuracy of the proposed scheme.}
}