First-order fractional step finite element method for the 2D/3D unstationary incompressible thermomicropolar fluid equations

In this paper, the first-order fractional step finite element method to solve the 2D/3D unstationary incompressible thermomicropolar fluid equations (ITME) is proposed. At each time step, the projection strategy about the linear velocity is adopted to get the linear velocity and pressure values in the first two sub-steps, and then the angular velocity and temperature values are solved in the last two sub-steps. Based on the proposed method, the variational problem is decomposed into four linear subproblems. By using the energy analysis technique, the unconditional stability and error estimates about the first-order semi-discrete method are derived, and the unconditional stability about the first-order fully discrete method is analyzed. Finally, some numerical experiments are carried out to show the feasibility and effectiveness of the method.