Analysis of three finite element iterative methods for the stationary magneto-micropolar equations

In this paper, three finite element iterative methods (Stokes, Newton and Oseen iterative methods) are proposed and analysed for the stationary magneto-micropolar equations (MME), which describe the motion of an incompressible, electrically conducting micropolar fluid in the presence of a magnetic field. Firstly, we derive the stability and error estimation for the Stokes and Newton iterative methods under the condition of strong uniqueness. With the weak uniqueness condition, the stability and error estimation for the Oseen iterative method are obtained. Furthermore, we prove that the Stokes and Newton iterative methods are stable and convergent, where the Newton iterative method has an exponential convergence rate with respect to the iterative step m. In particular, the Oseen iterative method is unconditionally stable and convergent. Numerical results confirm the accuracy of the theoretical findings and the effectiveness of the proposed methods.