Convergence of a - based finite element method for MHD models on Lipschitz domains
arXiv:1711.11330
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 estimate for divergence-free finite element functions for a new type of boundary conditions. With this estimate and a similar one in [Hu&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.
The original title was "Magnetic-Electric Formulations for Stationary Magnetohydrodynamics Models", revised version