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Constraint-Preserving Energy-Stable Scheme for the 2D Simplified Ericksen-Leslie System

Constraint-Preserving Energy-Stable Scheme for the 2D Simplified Ericksen-Leslie System
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Year:    2021

Author:    Xuelian Bao, Rui Chen, Hui Zhang

Journal of Computational Mathematics, Vol. 39 (2021), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1906-m2018-0144

Journal of Computational Mathematics, Vol. 39 (2021), Iss. 1 : pp. 1–21

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

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

Author Details

Xuelian Bao

Rui Chen

Hui Zhang

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