Geodesic
A two-grid method for an elliptic equation with boundary layers on a Shishkin mesh
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 49-56 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article, we consider a linear elliptic equation with regular and parabolic boundary layers. To solve this equation, we used an upwind difference scheme on a Shishkin mesh, possessing the property of the uniform convergence with respect to a small parameter. We investigated the problem of decreasing the required number of arithmetic operations for implementation of the difference scheme on the basis of a two-grid method, and studied the Richardson method aimed at improving the accuracy of this scheme. Here, we present results of some numerical experiments.
Mots-clés : elliptic equation, singular perturbation
Keywords: Shishkin mesh, difference scheme, iterative method, two-grid method, Richardson extrapolation. 
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     title = {A two-grid method for an elliptic equation with boundary layers on {a~Shishkin} mesh},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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S. V. Tikhovskaya. A two-grid method for an elliptic equation with boundary layers on a Shishkin mesh. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 49-56. http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a4/

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