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

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

Year:    2022

Author:    Pengzhan Huang, Yinnian He, Ting Li

Journal of Computational Mathematics, Vol. 40 (2022), Iss. 1 : pp. 26–43

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

Journal of Computational Mathematics, Vol. 40 (2022), Iss. 1 : pp. 26–43

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

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

Author Details

Pengzhan Huang

Yinnian He

Ting Li