Geodesic
A note on a generalized Shishkin-type mesh
Novi Sad Journal of Mathematics, Tome 48 (2018) no. 2.

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The one-dimensional linear singularly perturbed convection-diffusion problem is discretized using the upwind scheme on a mesh which is a mild generalization of Shishkin-type meshes. The generalized mesh uses the transition point of the Shishkin mesh, but it does not require any structure of its fine and course parts. Convergence uniform in the perturbation parameter is proved by the barrier-function technique, which, because of the unstructured mesh, does not rely on any mesh-generating function. In this way, the technical requirements needed in the existing barrier-function approaches are simplified.
Publié le :
DOI : 10.30755/NSJOM.07880
Classification : 65L10, 65L12, 65L20, 65L70
Keywords: boundary-value problem, singular perturbation, convection-diffusion, Shishkin-type meshes, finite differences, uniform convergence 
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     title = {A note on a generalized {Shishkin-type} mesh},
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     doi = {10.30755/NSJOM.07880},
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Thái Anh Nhan; Relja Vulanović. A note on a generalized Shishkin-type mesh. Novi Sad Journal of Mathematics, Tome 48 (2018) no. 2. doi : 10.30755/NSJOM.07880. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.07880/

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