Analysis of Local and Parallel Algorithm for Incompressible Magnetohydrodynamics Flows by Finite Element Iterative Method

Based on two-grid discretizations, a local and parallel finite element algorithm (LPFEA) based on Newton iteration for solving the stationary incompressible magnetohydrodynamics (MHD) is considered in this paper. The basic idea of the algorithm is to compute the nonlinear system by Newton iteration on a globally coarse mesh first, then solve a series of subproblems of residual correction on the corresponding subdomains with fine grids in parallel. The optimal error estimates with respective to iterative step m and mesh sizes H and h << H are derived. The efficiency of the method is illustrated by numerical experiments.