Nonhomogeneous MHD equations: convergence of semi-Galerkin approximations

Abstract We investigate the convergence rate of semi-Galerkin approximations for the magnetohydrodynamics equations with variable density. We obtain error estimates for the velocity, magnetic field, and density, and derive improved $${\\varvec{L}}^2$$ L 2 error bounds. Our results extend to the variable-density MHD system the convergence theory previously known for the classical and variable-density Navier-Stokes equations.