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Journal of Scientific Computing

, Volume 74, Issue 2, pp 979–1008 | Cite as

Optimal Error Estimates of Semi-implicit Galerkin Method for Time-Dependent Nematic Liquid Crystal Flows

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Abstract

This paper focuses on the optimal error estimates of a linearized semi-implicit scheme for the nematic liquid crystal flows, which is used to describe the time evolution of the materials under the influence of both the flow velocity and the microscopic orientation configurations of rod-like liquid crystal flows. Optimal error estimates of the scheme are proved without any restriction of time step by using an error splitting technique proposed by Li and Sun. Numerical results are provided to confirm the theoretical analysis and the stability of the semi-implicit scheme.

Keywords

Nematic liquid crystal model Linearized semi-implicit scheme Finite element method Optimal error estimates 

Mathematics Subject Classification

65M12 65M60 35Q35 

Notes

Acknowledgements

Rong An was supported by Zhejiang Provincial Natural Science Foundation with Grant No. LY16A010017. Jian Su was supported by National Natural Science Foundation of China with Grant No. 91330117.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceWenzhou UniversityWenzhouChina
  2. 2.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina

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