Two-Level Coupled and Decoupled Parallel Correction Methods for Stationary Incompressible Magnetohydrodynamics

Abstract

In this paper, we propose two-level coupled correction and decoupled parallel correction finite element methods for solving the stationary magnetohydrodynamics (MHD) equations. We prove the error estimates for the methods which show that if coarse mesh size $$(H)$$(H) and fine mesh size $$(h)$$(h) satisfy the relation $$H=O(\sqrt{h})$$H=O(h), the methods provide optimal convergence rates. Further, we study the dependence of the errors of the methods on parameters. Numerically, investigations for 2D/3D Hartmann flows with different physical parameters are conducted to validate theoretical analyses, which show the efficiency of the methods to solve the MHD problems.