In the paper we develop some two-level finite element iterative methods and use these methods to solve the stationary incompressible magnetohydrodynamics (MHD) with different Reynolds numbers under some different uniqueness conditions. Firstly, we use the Stokes type iterative method, Newton type iterative method and Oseen type iterative method of m times on a coarse mesh with mesh size H and then solve a linear problem with the Stokes type, Newton type and Oseen type correction of one time on a fine grid with mesh sizes h H. Furthermore, we analyze the uniform stability and convergence of these methods with respect to Reynolds numbers, mesh sizes h and H and iterative times m. Finally, the stationary incompressible MHD equations with large Reynolds number are researched by the one-level finite element method based on the Oseen type iteration on a fine mesh under a weak uniqueness condition.

We study the numerical methods for time-dependent natural convection problem that models coupled fluid flow and temperature field. A coupled numerical scheme is analyzed for the considered problem based on the backward Euler scheme; stability and the corresponding optimal error estimates are presented. Furthermore, a decoupled numerical scheme is proposed by decoupling the nonlinear terms via temporal extrapolation; optimal error estimates are established. Finally, some numerical results are provided to verify the performances of the developed algorithms. Compared with the coupled numerical scheme, the decoupled algorithm not only keeps good accuracy but also saves a lot of computational cost. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled method for time-dependent natural convection problem.

No abstract

No abstract

No abstract