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Volume 40, Issue 1
A Finite Element Algorithm for Nematic Liquid Crystal Flow Based on the Gauge-Uzawa Method

Pengzhan Huang, Yinnian He & Ting Li

DOI: 10.4208/jcm.2005-m2020-0010

J. Comp. Math., 40 (2022), pp. 26-43.

Published online: 2021-11

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hpzh007@yahoo.com (Pengzhan Huang)

heyn@mail.xjtu.edu.cn (Yinnian He)

1003887017@qq.com (Ting Li)

  • BibTex
  • RIS
  • TXT
@Article{JCM-40-26, author = {Huang , PengzhanHe , Yinnian and Li , Ting}, title = {A Finite Element Algorithm for Nematic Liquid Crystal Flow Based on the Gauge-Uzawa Method}, journal = {Journal of Computational Mathematics}, year = {2021}, volume = {40}, number = {1}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2005-m2020-0010}, url = {http://global-sci.org/intro/article_detail/jcm/19968.html} }
TY - JOUR T1 - A Finite Element Algorithm for Nematic Liquid Crystal Flow Based on the Gauge-Uzawa Method AU - Huang , Pengzhan AU - He , Yinnian AU - Li , Ting JO - Journal of Computational Mathematics VL - 1 SP - 26 EP - 43 PY - 2021 DA - 2021/11 SN - 40 DO - http://doi.org/10.4208/jcm.2005-m2020-0010 UR - https://global-sci.org/intro/article_detail/jcm/19968.html KW - Nematic liquid crystal model, Finite element approximation, Gauge-Uzawa method, Error analysis. AB -

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.

Huang , PengzhanHe , Yinnian and Li , Ting. (2021). A Finite Element Algorithm for Nematic Liquid Crystal Flow Based on the Gauge-Uzawa Method. Journal of Computational Mathematics. 40 (1). 26-43. doi:10.4208/jcm.2005-m2020-0010
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