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

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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. 
@article{UZKU_2012_154_4_a4,
     author = {S. V. Tikhovskaya},
     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},
     pages = {49--56},
     publisher = {mathdoc},
     volume = {154},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a4/}
}
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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/