Geodesic
Investigation of a two-grid method of improved accuracy for the elliptic reaction–diffusion equation with boundary layers
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 60-74

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A two-grid method for the elliptic equation with a small parameter $\varepsilon$ multiplying the highest derivative is investigated. The $\varepsilon$-uniformly convergent difference scheme on the Shishkin mesh is considered. To resolve the difference scheme, a two-grid method with $\varepsilon$-uniform interpolation formula is used. To increase the accuracy of the scheme, the Richardson extrapolation in the two-grid method is applied. The results of numerical experiments are discussed. Various iterative methods for implementation of the two-grid algorithm are suggested.
Mots-clés : elliptic reaction–diffusion equation, singular perturbation, uniform convergence.
Keywords: Shishkin mesh, two-grid method, Richardson extrapolation 
@article{UZKU_2015_157_1_a6,
     author = {S. V. Tikhovskaya},
     title = {Investigation of a~two-grid method of improved accuracy for the elliptic reaction{\textendash}diffusion equation with boundary layers},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {60--74},
     publisher = {mathdoc},
     volume = {157},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a6/}
}
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S. V. Tikhovskaya. Investigation of a two-grid method of improved accuracy for the elliptic reaction–diffusion equation with boundary layers. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 60-74. http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a6/