# Stable upwind schemes for the magnetic induction equation

Franz G. Fuchs; Kenneth H. Karlsen; Siddharta Mishra; Nils H. Risebro

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

- Volume: 43, Issue: 5, page 825-852
- ISSN: 0764-583X

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topFuchs, Franz G., et al. "Stable upwind schemes for the magnetic induction equation." ESAIM: Mathematical Modelling and Numerical Analysis 43.5 (2009): 825-852. <http://eudml.org/doc/250586>.

@article{Fuchs2009,

abstract = {
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.
},

author = {Fuchs, Franz G., Karlsen, Kenneth H., Mishra, Siddharta, Risebro, Nils H.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Conservation laws; induction equation; divergence constraint; upwinded source terms; conservation laws},

language = {eng},

month = {4},

number = {5},

pages = {825-852},

publisher = {EDP Sciences},

title = {Stable upwind schemes for the magnetic induction equation},

url = {http://eudml.org/doc/250586},

volume = {43},

year = {2009},

}

TY - JOUR

AU - Fuchs, Franz G.

AU - Karlsen, Kenneth H.

AU - Mishra, Siddharta

AU - Risebro, Nils H.

TI - Stable upwind schemes for the magnetic induction equation

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2009/4//

PB - EDP Sciences

VL - 43

IS - 5

SP - 825

EP - 852

AB -
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.

LA - eng

KW - Conservation laws; induction equation; divergence constraint; upwinded source terms; conservation laws

UR - http://eudml.org/doc/250586

ER -

## References

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