The purpose of this paper is to propose a local parallel finite element algorithm based on fully overlapping domain decomposition technique to solve the incompressible magnetohydrodynamic equations.
The algorithm uses a lower-order element pair to compute an initial approximation by the Oseen-type iteration and uses a higher-order element pair to solve a linear system in each processor.
Besides, the convergence analysis of local parallel finite element algorithm is given. Finally, numerical experiments are presented to verify the efficiency of the proposed algorithm.
Compared with the numerical solution of the common two-step method, this method is easy to realize and can produce a more accurate solution. And, this approach is executed in parallel, so it saves a lot of computational time.
