A Finite Element Algorithm for Nematic Liquid Crystal Flow Based on the Gauge-Uzawa Method

Authors

  • Pengzhan Huang College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
  • Yinnian He School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, P. R. China
  • Ting Li College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China

DOI:

https://doi.org/10.4208/jcm.2005-m2020-0010

Keywords:

Nematic liquid crystal model, Finite element approximation, Gauge-Uzawa method, Error analysis.

Abstract

In this paper, we present a finite element algorithm for the time-dependent nematic liquid crystal flow based on the Gauge-Uzawa method. This algorithm combines the Gauge and Uzawa methods within a finite element variational formulation, which is a fully discrete projection type algorithm, whereas many projection methods have been studied without space discretization. Besides, error estimates for velocity and molecular orientation of the nematic liquid crystal flow are shown. Finally, numerical results are given to show that the presented algorithm is reliable and confirm the theoretical analysis.

Downloads

Published

2021-11-19

Issue

Vol. 40 No. 1 (2022)

Section

Articles