Convergence Analysis of Some Finite Element Parallel Algorithms for the Stationary Incompressible MHD Equations (Journal of Computational Mathematics, 2023)
By combination of iteration methods with the partition of unity method (PUM), somefinite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD) with different physical parameters are presented and analyzed. These algorithmsare highly efficient. At first, a global solution is obtained on a coarse grid for all approachesby one of the iteration methods. By parallelized residual schemes, local corrected solutionsare calculated on finer meshes with overlapping sub-domains. The subdomains can beachieved flexibly by a class of PUM. The proposed algorithm is proved to be uniformlystable and convergent. Finally, one numerical example is presented to confirm the theoretical findings.