向列相液晶流的模块grad-div稳定化有限元方法

数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 451-467.

向列相液晶流的模块grad-div稳定化有限元方法

李婷(),黄鹏展*()

^{新疆大学数学与系统科学学院乌鲁木齐 830046}

收稿日期:2020-02-25 出版日期:2021-04-26 发布日期:2021-04-29
通讯作者: 黄鹏展 E-mail:lt1003887017@163.com;hpzh007@yahoo.com
作者简介:李婷, E-mail: lt1003887017@163.com
基金资助:
国家自然科学基金(11861067)

A Modular grad-div Stabilized Finite Element Method for Nematic Liquid Crystal Flow

Ting Li(),Pengzhan Huang*()

^{College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046}

Received:2020-02-25 Online:2021-04-26 Published:2021-04-29
Contact: Pengzhan Huang E-mail:lt1003887017@163.com;hpzh007@yahoo.com
Supported by:
the NSFC(11861067)

摘要/Abstract

摘要：

该文针对向列相液晶流，提出了一种模块grad-div稳定化有限元方法，主要是在向后欧拉格式中增加了一个后处理步骤.该方法可以惩罚原有格式的质量不守恒性，但不会随着稳定化参数的变大而使计算时间增加.此外，该文给出了向列相液晶流的速度和分子方向的误差估计，还通过数值实验验证了理论分析.

关键词: 向列相液晶模型, 模块grad-div稳定化方法, 误差分析, 有限元方法, 向后欧拉方法

Abstract:

In this paper, we presents a modular grad-div stabilized finite element method for nematic liquid crystal flow, which adds to the backward Euler scheme a post precessing step. This method can penalize for lack of mass conservation but it does not increase computational time for increasing stabilized parameters. Moreover, error estimates for velocity and molecular orientation of the nematic liquid crystal flow are shown. Finally, the theoretical findings and numerical efficiency are verified by numerical experiments.

Key words: Nematic liquid crystal model, Modular grad-div stabilized method, Error estimates, Finite element method, Backward Euler scheme

中图分类号:

O242

李婷,黄鹏展. 向列相液晶流的模块grad-div稳定化有限元方法[J]. 数学物理学报, 2021, 41(2): 451-467.

Ting Li,Pengzhan Huang. A Modular grad-div Stabilized Finite Element Method for Nematic Liquid Crystal Flow[J]. Acta mathematica scientia,Series A, 2021, 41(2): 451-467.

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