  We propose a new mixed finite element method for the three-dimensional steady
magnetohydrodynamic (MHD) kinematics equations for which the velocity of the
fluid is given. Although prescribing the velocity field leads to a simpler
model than full MHD equations, its conservative and efficient numerical methods
are still active research topic. The distinctive feature of our discrete scheme
is that the divergence-free conditions for current density and magnetic
induction are both satisfied. To reach this goal, we use magnetic vector
potential to represent magnetic induction and resort to H(div)-conforming
element to discretize the current density. We develop an preconditioned
iterative solver based on a block preconditioner for the algebraic systems
arising from the discretization. Several numerical experiments are implemented
to verify the divergence-free properties, the convergence rate of the finite
element scheme and the robustness of the preconditioner.
