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

Cheng Liao, Danxia Wang () and Haifeng Zhang
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Cheng Liao: School of Mathematics, Taiyuan University of Technology, Jinzhong 030600, China
Danxia Wang: School of Mathematics, Taiyuan University of Technology, Jinzhong 030600, China
Haifeng Zhang: School of Mathematics, Taiyuan University of Technology, Jinzhong 030600, China

Mathematics, 2024, vol. 12, issue 5, 1-23

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.

Keywords: Ericksen–Leslie model; convex splitting method; backward differentiation formula; leap frog method; unconditional energy stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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