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Volume 39, Issue 1
Constraint-Preserving Energy-Stable Scheme for the 2D Simplified Ericksen-Leslie System

Xuelian Bao, Rui Chen & Hui Zhang

DOI: 10.4208/jcm.1906-m2018-0144

J. Comp. Math., 39 (2021), pp. 1-21.

Published online: 2020-09

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  • Abstract

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.

  • Keywords

Nematic liquid crystal, Ericksen-Leslie system, Constraint preserving, Finite element.

  • AMS Subject Headings

52B10, 65D18, 68U05, 68U07

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xuelian_bao@163.com (Xuelian Bao)

ruichenbnu@gmail.com (Rui Chen)

hzhang@bnu.edu.cn (Hui Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-39-1, author = {Bao , XuelianChen , Rui and Zhang , Hui}, title = {Constraint-Preserving Energy-Stable Scheme for the 2D Simplified Ericksen-Leslie System}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {39}, number = {1}, pages = {1--21}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1906-m2018-0144}, url = {http://global-sci.org/intro/article_detail/jcm/18275.html} }
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 -

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.

Bao , XuelianChen , Rui and Zhang , Hui. (2020). Constraint-Preserving Energy-Stable Scheme for the 2D Simplified Ericksen-Leslie System. Journal of Computational Mathematics. 39 (1). 1-21. doi:10.4208/jcm.1906-m2018-0144
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