Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations

Based on local algorithms, some parallel finite element (FE) iterative methods for stationary incompressible magnetohydrodynamics (MHD) are presented. These approaches are on account of two-grid skill include two major phases: find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution, and then locally solve linearized residual subproblems by one of three iterations (Stokes-type, Newton, and Oseen-type) on subdomains with fine grid in parallel to approximate the high frequency component. Optimal error estimates with regard to two mesh sizes and iterative steps of the proposed algorithms are given. Some numerical examples are implemented to verify the algorithm.