A priori estimates of the unsteady incompressible thermomicropolar fluid equations and its numerical analysis based on penalty finite element method.

In this paper, the unsteady incompressible thermomicropolar fluid (UITF) equations are considered. Theoretically, some a priori regularity conclusions are presented firstly, which seem to be not available in the literatures. Numerically, a penalty finite element method (PFEM) for the UITF equations is studied, the Euler semi-implicit temporal semi-discrete method of the penalty UITF equations is proposed, the stability and the L 2 - H 1 error estimates of the temporal discrete solutions are proved. Finally, the stability and the L 2 - H 1 error estimates for the finite element fully-discrete approximation of the penalty UITF equations are rigorously proved. The accuracy and efficiency of the fully-discrete PFEM are demonstrated by some numerical examples. • This paper focus on penalty method for unsteady incompressible thermomicropolar fluid equations. • Some a priori regularity conclusions are presented. • Stability and L 2 − H 1 error estimates of Euler semi-implicit method are proposed. • Stability and L 2 − H 1 error estimates of fully-discrete method are proved. [ABSTRACT FROM AUTHOR]