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The Second-Order Numerical Approximation for a Modified Ericksen–Leslie Model

Author

Listed:
  • Cheng Liao

    (School of Mathematics, Taiyuan University of Technology, Jinzhong 030600, China
    These authors contributed equally to this work.)

  • Danxia Wang

    (School of Mathematics, Taiyuan University of Technology, Jinzhong 030600, China
    Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology, Taiyuan 030024, China
    These authors contributed equally to this work.)

  • Haifeng Zhang

    (School of Mathematics, Taiyuan University of Technology, Jinzhong 030600, China
    These authors contributed equally to this work.)

Abstract

In this study, two numerical schemes with second-order accuracy in time for a modified Ericksen–Leslie model are constructed. The highlight is based on a novel convex splitting method for dealing with the nonlinear potentials, which is integrated with the second-order backward differentiation formula (BDF2) and leap frog method for temporal discretization and the finite element method for spatial discretization. The unconditional energy stability of both schemes is further demonstrated. Finally, several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed schemes.

Suggested Citation

  • Cheng Liao & Danxia Wang & Haifeng Zhang, 2024. "The Second-Order Numerical Approximation for a Modified Ericksen–Leslie Model," Mathematics, MDPI, vol. 12(5), pages 1-23, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:672-:d:1345597
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    References listed on IDEAS

    as
    1. Zhang, Xin & Wang, Danxia & Zhang, Jianwen & Jia, Hongen, 2023. "Fully decoupled linear BDF2 scheme for the penalty incompressible Ericksen–Leslie equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 249-266.
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