ETNA - Electronic Transactions on Numerical Analysis, pp. 63-82, 2025/02/03
This paper shows that, for the stationary thermally coupled incompressible magnetohydrodynamics problem, an application of the grad-div stabilization technique and a modification of the Arrow–Hurwicz iteration can improve the convergence rate of the Arrow–Hurwicz algorithm and remove restrictions on the relaxation parameter $\alpha$ for this algorithm. Based on the grad-div stabilization method, we design an Arrow–Hurwicz-type iterative finite element algorithm for solving this problem. A convergence analysis as well as numerical tests show that the proposed iteration performs better for the considered problem compared to the standard Arrow–Hurwicz iteration.
Keywords: Arrow–Hurwicz-type iteration, thermally coupled magnetohydrodynamics, grad-div stabilization, convergence analysis
