Investigation of a two-grid method of improved accuracy for the elliptic reaction–diffusion equation with boundary layers

S. V. Tikhovskaya

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 60-74

Résumé

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.

Détail

Mots-clés : elliptic reaction–diffusion equation, singular perturbation, uniform convergence.
Keywords: Shishkin mesh, two-grid method, Richardson extrapolation

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