On the existence, uniqueness, and finite element approximation of solutions of the equations of stationary, incompressible magnetohydrodynamics

The authors consider the equations of stationary, incompressible magneto-hydrodynamics posed in a bounded domain in three dimensions and treat the full, coupled system of equations with inhomogeneous boundary conditions. Under certain conditions on the data, they show that the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed. They discuss a finite element discretization of the equations and prove an optimal estimate for the error of the approximate solution