(untitled) (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 finite element scheme. We first establish some regularity results for the solution of MNSE, which seem to be not available in the literature. Next, we study a semi-implicit time-discrete scheme for the MNSE and prove L^2-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 L^2-H^1 error estimates for the finite element solution of MNSE. Finally, some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.