Effcient numerical methods for strongly anisotropic elliptic equations

Christophe Besse (1, 2) , Fabrice Deluzet (3) , Claudia Negulescu (4) , Chang Yang (1, 2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 SIMPAF - SImulations and Modeling for PArticles and Fluids
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 LATP - Laboratoire d'Analyse, Topologie, Probabilités

In this paper, we study an effcient numerical scheme for a strongly anisotropic elliptic problem which arises in the modeling of ionospheric plasma dynamics. A small parameter \varepsilon induces the anisotropy of the problem, which leads to severe numerical diffculties for 0 < \varepsilon

Mots clés: Anisotropic elliptic equation; Singular Perturbation Model; Asymptotic Preserving scheme; Scharfetter-Gummel scheme; Heterogeneous anisotropy ratios.; Heterogeneous anisotropy ratios

Domaines: Physique mathématique [math-ph]

Christophe Besse, Fabrice Deluzet, Claudia Negulescu, Chang Yang. Effcient numerical methods for strongly anisotropic elliptic equations. 2011. ⟨hal-00586031⟩