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

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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 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.

MSC

primary
65N30
76W05

Keywords

Magnetohydrodynamics
Finite element method
Structure-preserving
de Rham complex

Cited by (0)

☆

The title of this article in its original version (see arXiv:1711.11330) is “Magnetic-Electric Formulations for Stationary Magnetohydrodynamics Models”.

☆☆

As a convention the names of the authors are alphabetically ordered.

★

All authors contributed equally in this article.

1

The work of Kaibo Hu was partly carried out during his affiliation with the University of Oslo, supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement 339643.

2

Weifeng Qiu is partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region , China (Project No. CityU 11304017).

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