Penalty Finite Element Method for the 2D/3D Unsteady Incompressible Thermomicropolar Fluid Equations (Advances in Applied Mathematics and Mechanics, 2025)
In this paper, a first-order penalty finite element method for the 2D/3D unsteady incompressible thermomicropolar fluid (UITF) equations is considered, whichcombines 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 areadopted in concrete spatial discrete, and the feasibility of the method is verified bynumerical experiments.