Convergence of a $B$-$E$ based finite element method for MHD models on Lipschitz domains
Numerical Analysis
2019-05-03 v2
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.
Cite
@article{arxiv.1711.11330,
title = {Convergence of a $B$-$E$ based finite element method for MHD models on Lipschitz domains},
author = {Kaibo Hu and Weifeng Qiu and Ke Shi},
journal= {arXiv preprint arXiv:1711.11330},
year = {2019}
}
Comments
The original title was "Magnetic-Electric Formulations for Stationary Magnetohydrodynamics Models", revised version