In this paper we describe and analyze a two-level method for discretizing the equations of stationary, viscous, incompressible magnetohydrodynamics. The MHD equations model the flow of a viscous, incompressible, electrically conducting fluid, interacting with magnetic and electric fields. These arise in plasma physics, nuclear reactor technology, and geophysics.

The suggested algorithm involves solving a small nonlinear problem on a coarse mesh and then one large linear system on a fine mesh.