Geodesic
Uniformly convergent difference scheme for singularly perturbed problem of mixed type
Electronic transactions on numerical analysis, Tome 23 (2006), pp. 288-303
Zbl   EuDML
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 
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/
@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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TI  - Uniformly convergent difference scheme for singularly perturbed problem of mixed type
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SP  - 288
EP  - 303
VL  - 23
UR  - http://geodesic.mathdoc.fr/item/ETNA_2006__23__a3/
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%J Electronic transactions on numerical analysis
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