Unconditional Convergence and Error Estimates of a Fully Discrete Finite Element Method for the Micropolar Navier-Stokes Equations (Journal of Computational Mathematics, 2023)
In this paper, we consider the initial-boundary value problem (IBVP) for the micropolar Navier-Stokes equations (MNSE) and analyze a first order fully discrete mixed finiteelement scheme. We first establish some regularity results for the solution of MNSE, whichseem to be not available in the literature. Next, we study a semi-implicit time-discretescheme for the MNSE and prove $\boldsymbol{L}^2-\boldsymbol{H}^1$ error estimates for the time discrete solution. Furthermore, certain regularity results for the time discrete solution are established rigorously.Based on these regularity results, we prove the unconditional $\boldsymbol{L}^2-\boldsymbol{H}^1$ error estimates forthe finite element solution of MNSE. Finally, some numerical examples are carried out todemonstrate both accuracy and efficiency of the fully discrete finite element scheme.