Convergence of a [formula omitted]-[formula omitted] based finite element method for MHD models on Lipschitz domains

Abstract

We discuss a class of magnetic–electric fields based finite element schemes for stationary magnetohydrodynamics (MHD) systems with two types of boundary conditions. We establish a key L3 estimate for divergence-free finite element functions for a new type of boundary conditions. With this estimate and a similar one in Hu and Xu (2018), we rigorously prove the convergence of Picard iterations and the finite element schemes with weak regularity assumptions. These results demonstrate the convergence of the finite element methods for singular solutions.