  Magnetohydrodynamics (MHD) is a continuum level model for conducting fluids
subject to external magnetic fields, e.g. plasmas and liquid metals. The
efficient and robust solution of the MHD system poses many challenges due to
it's nonlinear, non self-adjoint, and highly coupled nature. In this paper, we
develop a robust and accurate a posteriori error estimate for the numerical
solution of the MHD equations based on the exact penalty method. The error
estimate also isolates particular contributions of error in a quantity of
interest (QoI) to inform discretization choices to arrive at accurate
solutions. The tools required for these estimates involve duality arguments and
computable residuals.
