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arXiv · 1711.11330

Convergence of a $B$-$E$ based finite element method for MHD models on Lipschitz domains

Kaibo Hu·Weifeng Qiu·Ke Shi
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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 $L^{3}$ 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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Kaibo Hu, Weifeng Qiu, Ke Shi. 2017-11-30. Convergence of a $B$-$E$ based finite element method for MHD models on Lipschitz domains. https://arxiv.org/abs/1711.11330

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