Numerical analysis of Backward-Euler discretization for simplified magnetohydrodynamic flows

Magnetohydrodynamics (MHD) studies consider the dynamics of electrically conducting fluids. MHD are described by a set of equations, which are a combination of the Navier-Stokes equations of fluid dynamics and Maxwell's equations of electromagnetism. In most terrestrial applications, MHD flows occur at low magnetic Reynolds numbers. In this study, we apply the finite element method to time-dependent MHD flows with Backward-Euler discretization at low magnetic Reynolds number. We present a comprehensive error analysis for fully discrete approximation. Finally, the effectiveness of the method is illustrated by several numerical examples.