Commun. Comput. Phys., 11 (2012), pp. 147-178.

Degenerate Anisotropic Elliptic Problems and Magnetized Plasma Simulations

Stephane Brull 1*, Pierre Degond 2, Fabrice Deluzet 2

1 Institut de Mathematiques de Bordeaux UMR 5251, Equipe Mathematiques Appliquees de Bordeaux (MAB) Universite Bordeaux 1 351, cours de la Liberation-33405 TALENCE cedex, France.
2 Universite de Toulouse; UPS, INSA, UT1, UTM; Institut de Mathematiques de Toulouse; F-31062 Toulouse, France; and CNRS; Institut de Mathematiques de Toulouse UMR 5219, F-31062 Toulouse, France.

Received 30 October 2010; Accepted (in revised version) 18 March 2011
Available online 5 September 2011


This paper is devoted to the numerical approximation of a degenerate anisotropic elliptic problem. The numerical method is designed for arbitrary space-dependent anisotropy directions and does not require any specially adapted coordinate system. It is also designed to be equally accurate in the strongly and the mildly anisotropic cases. The method is applied to the Euler-Lorentz system, in the drift-fluid limit. This system provides a model for magnetized plasmas.

AMS subject classifications: 65N06, 65N12, 65M06, 65M12, 76W05, 76X05, 76N17

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Key words: Anisotropic elliptic problem, asymptotic-preserving scheme, Lorentz force, large magnetic field, low-Mach number, drift-fluid limit.

*Corresponding author.
Email: (S. Brull), (P. Degond), (F. Deluzet)

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