Analysis of Local and Parallel Algorithm for Incompressible Magnetohydrodynamics Flows by Finite Element Iterative Method (Communications in Computational Physics, 2018)
Based on two-grid discretizations, a local and parallel finite element algorithm(LPFEA) based on Newton iteration for solving the stationary incompressiblemagnetohydrodynamics (MHD) is considered in this paper. The basic idea of the algorithmis to compute the nonlinear system by Newton iteration on a globally coarsemesh first, then solve a series of subproblems of residual correction on the correspondingsubdomains with fine grids in parallel. The optimal error estimates with respectiveto iterative step m and mesh sizes H and h≪H are derived. The efficiency of themethod is illustrated by numerical experiments.
Keywords: Local and parallel algorithm; finite element; Newton iteration; stationary incompressible magnetohydrodynamics.