The Arrow-Hurwicz Iterative Finite Element Method for the Stationary Thermally Coupled Incompressible Magnetohydrodynamics Flow

In this paper, we construct the Arrow-Hurwicz iterative finite element method for solving the stationary thermally coupled incompressible magnetohydrodynamics system, where a decoupled discrete system is obtained and no saddle point problem is required to deal with at each iterative step. Under several conditions, it is proved that the iterative solution solved by the proposed iterative method is convergent. Finally, the effectiveness of the considered iterative method is illustrated with some numerical examples.

Automated summary

In this paper, the Arrow-Hurwicz iterative finite element method is proposed to solve the stationary thermally coupled incompressible magnetohydrodynamics system. It is proven that the iterative solution obtained by this method is convergent under certain conditions, and the effectiveness is illustrated with numerical examples.