(untitled) (Journal of Computational Mathematics, 2021)
In this paper, we present a finite element algorithm for the time-dependent nematic liquid crystal flow based on the Gauge-Uzawa method. This algorithm combines the Gauge and Uzawa methods within a finite element variational formulation, which is a fully discrete projection type algorithm, whereas many projection methods have been studied without space discretization. Besides, error estimates for velocity and molecular orientation of the nematic liquid crystal flow are shown. Finally, numerical results are given to show that the presented algorithm is reliable and confirm the theoretical analysis.