TY - JOUR
T1 - Unconditional Convergence and Error Estimates of a Fully Discrete Finite Element Method for the Micropolar Navier-Stokes Equations
AU - Mao , Shipeng
AU - Sun , Jiaao
AU - Xue , Wendong
JO - Journal of Computational Mathematics
VL - 1
SP - 71
EP - 110
PY - 2023
DA - 2023/12
SN - 42
DO - http://doi.org/10.4208/jcm.2201-m2021-0315
UR - https://global-sci.org/intro/article_detail/jcm/22153.html
KW - Micropolar fluids, Regularity estimates, Euler semi-implicit scheme, Mixed
finite element methods, Unconditional convergence.
AB - <p style="text-align: justify;">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 $\boldsymbol{L}^2-\boldsymbol{H}^1$ 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 $\boldsymbol{L}^2-\boldsymbol{H}^1$&nbsp;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.</p>