  In this paper, we propose a robust solver for the finite element discrete
problem of the stationary incompressible magnetohydrodynamic (MHD) equations in
three dimensions. By the mixed finite element method, both the velocity and the
pressure are approximated by H1-conforming finite elements, while the magnetic
field is approximated by H(curl)-conforming edge elements. An efficient
preconditioner is proposed to accelerate the convergence of the GMRES method
for solving the linearized MHD problem. We use three numerical experiments to
demonstrate the effectiveness of the finite element method and the robustness
of the discrete solver. The preconditioner contains the least undetermined
parameters and is optimal with respect to the number of degrees of freedom. We
also show the scalability of the solver for moderate physical parameters.
