Geodesic
Uniformly convergent difference scheme for singularly perturbed problem of mixed type
Electronic transactions on numerical analysis, Tome 23 (2006), pp. 288-303
A one dimensional singularly perturbed elliptic problem with discontinuous coefficients is considered. The domain under consideration is partitioned into two subdomains. In the first subdomain a convectiondiffusion-reaction equation is posed. In the second one we have a pure reaction-diffusion equation. The problem is discretized using an inverse-monotone finite volume method on Shishkin meshes. We establish an almost second-order global pointwise convergence that is uniform with respect to the perturbation parameter. Numerical experiments that support the theoretical results are given.
Classification : 34A36, 34E05, 34E15, 65L10, 65L12, 65L20, 65L50
Keywords: convection-diffusion problems, singular perturbation, asymptotic analysis, finite volume methods, modified upwind approximations, uniform convergence, shishkin mesh 
@article{ETNA_2006__23__a3,
     author = {Brayanov,  Iliya A.},
     title = {Uniformly convergent difference scheme for singularly perturbed problem of mixed type},
     journal = {Electronic transactions on numerical analysis},
     pages = {288--303},
     year = {2006},
     volume = {23},
     zbl = {1112.65073},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__23__a3/}
}
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AU  - Brayanov,  Iliya A.
TI  - Uniformly convergent difference scheme for singularly perturbed problem of mixed type
JO  - Electronic transactions on numerical analysis
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EP  - 303
VL  - 23
UR  - http://geodesic.mathdoc.fr/item/ETNA_2006__23__a3/
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%0 Journal Article
%A Brayanov,  Iliya A.
%T Uniformly convergent difference scheme for singularly perturbed problem of mixed type
%J Electronic transactions on numerical analysis
%D 2006
%P 288-303
%V 23
%U http://geodesic.mathdoc.fr/item/ETNA_2006__23__a3/
%G en
%F ETNA_2006__23__a3
Brayanov,  Iliya A. Uniformly convergent difference scheme for singularly perturbed problem of mixed type. Electronic transactions on numerical analysis, Tome 23 (2006), pp. 288-303. http://geodesic.mathdoc.fr/item/ETNA_2006__23__a3/