Adv. Appl. Math. Mech., 17 (2025), pp. 1509-1549.
Published online: 2025-07
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In this paper, a first-order penalty finite element method for the 2D/3D unsteady incompressible thermomicropolar fluid (UITF) equations is considered, which combines the advantage of the penalty method, first-order backward Euler scheme, and implicit or explicit iteration for the nonlinear terms to get a decoupled temporal evolution procedure, which only needs to solve a series of elliptic subproblems. Theoretically, the stability analysis and optimal error estimates of the temporal semi-discrete method are deduced. Furthermore, the classical MINI element pairs are adopted in concrete spatial discrete, and the feasibility of the method is verified by numerical experiments.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0238}, url = {http://global-sci.org/intro/article_detail/aamm/24290.html} }In this paper, a first-order penalty finite element method for the 2D/3D unsteady incompressible thermomicropolar fluid (UITF) equations is considered, which combines the advantage of the penalty method, first-order backward Euler scheme, and implicit or explicit iteration for the nonlinear terms to get a decoupled temporal evolution procedure, which only needs to solve a series of elliptic subproblems. Theoretically, the stability analysis and optimal error estimates of the temporal semi-discrete method are deduced. Furthermore, the classical MINI element pairs are adopted in concrete spatial discrete, and the feasibility of the method is verified by numerical experiments.