Geodesic
A uniformly accurate finite volume discretization for a convection-diffusion problem
Electronic transactions on numerical analysis, Tome 13 (2002), pp. 1-11
A singularly perturbed convection-diffusion problem is considered. The problem is discretized using an inverse-monotone finite volume method on Shishkin meshes. We establish first-order convergence in a global energy norm and a mesh-dependent discrete energy norm, no matter how small the perturbation parameter. Numerical experiments support the theoretical results.
Classification : 65N30
Keywords: convection-diffusion problems, finite volume methods, singular perturbation, shishkin mesh 
@article{ETNA_2002__13__a7,
     author = {Wollstein,  Dirk and Lin{\ss},  Torsten and Roos,  Hans-G\"org},
     title = {A uniformly accurate finite volume discretization for a convection-diffusion problem},
     journal = {Electronic transactions on numerical analysis},
     pages = {1--11},
     year = {2002},
     volume = {13},
     zbl = {1024.65108},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2002__13__a7/}
}
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AU  - Roos,  Hans-Görg
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%A Roos,  Hans-Görg
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%J Electronic transactions on numerical analysis
%D 2002
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%G en
%F ETNA_2002__13__a7
Wollstein,  Dirk; Linß,  Torsten; Roos,  Hans-Görg. A uniformly accurate finite volume discretization for a convection-diffusion problem. Electronic transactions on numerical analysis, Tome 13 (2002), pp. 1-11. http://geodesic.mathdoc.fr/item/ETNA_2002__13__a7/