On a two-order temporal scheme for Navier-Stokes/Navier-Stokes equations

Abstract

In this paper, a fully discrete finite element scheme with two-order temporal accuracy is proposed for the Navier-Stokes/Navier-Stokes equations, which consists of two Navier-Stokes equations coupled by a linear interface condition. The considered scheme includes two steps: In the first step, a fully discrete first-order backward Euler scheme is given based on the mixed finite element method. Then, in the second step, a postprecessing step is designed for the velocity and pressure, which does not increase some computational complexity. Moreover, the stability and error estimates of the fully discrete scheme are established. Finally, numerical experiments are provided to verify both theoretical findings and efficiency of the presented scheme.