Geodesic
Stable upwind schemes for the magnetic induction equation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 5, pp. 825-852

Voir la notice de l'article provenant de la source Numdam

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 : 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 },
     pages = {825--852},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {5},
     year = {2009},
     doi = {10.1051/m2an/2009006},
     mrnumber = {2559735},
     zbl = {1177.78057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2009006/}
}
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 
PY  - 2009
SP  - 825
EP  - 852
VL  - 43
IS  - 5
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2009006/
DO  - 10.1051/m2an/2009006
LA  - en
ID  - M2AN_2009__43_5_825_0
ER  - 
%0 Journal Article
%A Fuchs, Franz G.
%A Karlsen, Kenneth H.
%A Mishra, Siddharta
%A Risebro, Nils H.
%T Stable upwind schemes for the magnetic induction equation
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2009
%P 825-852
%V 43
%N 5
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2009006/
%R 10.1051/m2an/2009006
%G en
%F 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 , Tome 43 (2009) no. 5, pp. 825-852. doi: 10.1051/m2an/2009006

Cité par Sources :