Convergence of a B-E 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&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.
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