Unconditional Convergence and Error Estimates of a Fully Discrete Finite Element Method for the Micropolar Navier-Stokes Equations
Year: 2024
Author: Shipeng Mao, Jiaao Sun, Wendong Xue
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 71–110
Abstract
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 $\boldsymbol{L}^2-\boldsymbol{H}^1$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2201-m2021-0315
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 71–110
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 40
Keywords: Micropolar fluids Regularity estimates Euler semi-implicit scheme Mixed finite element methods Unconditional convergence.