Stable upwind schemes for the magnetic induction equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 5, p. 825-852

We consider the magnetic induction equation for the evolution of a magnetic field in a plasma where the velocity is given. The aim is to design a numerical scheme which also handles the divergence constraint in a suitable manner. We design and analyze an upwind scheme based on the symmetrized version of the equations in the non-conservative form. The scheme is shown to converge to a weak solution of the equations. Furthermore, the discrete divergence produced by the scheme is shown to be bounded. We report several numerical experiments that show that the stable upwind scheme of this paper is robust.

DOI : https://doi.org/10.1051/m2an/2009006
Classification:  65M12,  35L65
Keywords: conservation laws, induction equation, divergence constraint, upwinded source terms
@article{M2AN_2009__43_5_825_0,
     author = {Fuchs, Franz G. and Karlsen, Kenneth H. and Mishra, Siddharta and Risebro, Nils H.},
     title = {Stable upwind schemes for the magnetic induction equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {5},
     year = {2009},
     pages = {825-852},
     doi = {10.1051/m2an/2009006},
     zbl = {1177.78057},
     mrnumber = {2559735},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2009__43_5_825_0}
}
Fuchs, Franz G.; Karlsen, Kenneth H.; Mishra, Siddharta; Risebro, Nils H. Stable upwind schemes for the magnetic induction equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 5, pp. 825-852. doi : 10.1051/m2an/2009006. http://www.numdam.org/item/M2AN_2009__43_5_825_0/

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