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

Authors

  • Xuelian Bao School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
  • Rui Chen School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
  • Hui Zhang School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, 100875, China

DOI:

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

Keywords:

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

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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Published

2021-06-10

Issue

Vol. 39 No. 1 (2021)

Section

Articles