An efficient two-step algorithm for the stationary incompressible magnetohydrodynamic equations

A new highly efficient two-step algorithm for the stationary incompressible magnetohydrodynamic equations is studied in this paper. The algorithm uses a lower order finite element pair (i.e., P 1 b - P 1 - P 1 ) to compute an initial approximation, that is using the Mini-element (i.e., P 1 b - P 1 ) to approximate the velocity and pressure and P1 element to approximate the magnetic field, then applies a higher order finite element pair (i.e., P 2 - P 1 - P 2 ) to solve a linear system on the same mesh. Furthermore, the convergence analyses of standard Galerkin finite element method and the two-step algorithm are addressed. Lastly, numerical experiments are presented to verify both the theory and the efficiency of the algorithm.

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