AN A POSTERIORI ERROR ANALYSIS FOR THE EQUATIONS OF STATIONARY INCOMPRESSIBLE MAGNETOHYDRODYNAMICS

Resistive magnetohydrodynamics (MHD) is a continuum base-level model for conducting fluids (e.g., plasmas and liquid metals) subject to external magnetic fields. The efficient and robust solution of the MHD system poses many challenges due to the strongly nonlinear, non-self-adjoint, and highly coupled nature of the physics. In this article, we develop a robust and accurate a posteriori error estimate for the numerical solution of the resistive MHD equations based on the exact penalty method. The error estimate also isolates particular contributions to the 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.