Penalty Finite Element Method for the 2D/3D Unsteady Incompressible Thermomicropolar Fluid Equations

Abstract

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.