A posteriori error estimation for two level discretizations of flows of electrically conducting, incompressible fluids

We develop a posteriori error estimates for two finite element discretizations of a model, due to Peterson [1], describing the flow of an electrically conducting, viscous incompressible fluid. The model involves five equations for the fluid velocity u, the pressure p and the electric potential. Estimates are derived for both the usual finite element method as well as a two level Newton finite element discretization.