Geodesic
Numerical simulations of boundary layer problems
Matematičeskoe modelirovanie, Tome 27 (2015) no. 11, pp. 47-55.

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At the interface between two media there often appear boundary layers. Singularly perturbed Helmholz equation is typical example. Up-to-date finite difference methods are shown to be capable of effective solving of such problems. Convergence verification procedure is proposed that does not require a priori estimations construction. A superfast algorithm that provides a posteriori asymptotically precise error estimation is described and semi-uniform rectangular grid that resolves all parts of solution is proposed. The algorithm proposed makes it possible to achieve good precisions on moderate grids with number of points $N\sim 200$ in each direction. This algorithm is realized as a program in Matlab environment.
Keywords: singularly perturbed problems, Helmholz equation, Richardson method.
Mots-clés : error estimation 
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A. A. Belov; N. N. Kalitkin. Numerical simulations of boundary layer problems. Matematičeskoe modelirovanie, Tome 27 (2015) no. 11, pp. 47-55. http://geodesic.mathdoc.fr/item/MM_2015_27_11_a3/

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