A Fully Discrete, Decoupled Scheme with Different Time Steps for Approximating Nematic Liquid Crystal Flow

Abstract

This paper designs a decoupled scheme for approximating nematic liquid crystal flow based on a fully discrete mixed finite element method, which allows different time steps for different physical fields. Besides, error estimates for velocity and macroscopic molecular orientation of the nematic liquid crystal flow are shown. Finally, numerical tests are provided to demonstrate efficiency of the scheme. It is found the presented scheme can save lots of computational time compared with common decoupled scheme.