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 
@article{MM_2015_27_11_a3,
     author = {A. A. Belov and N. N. Kalitkin},
     title = {Numerical simulations of boundary layer problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {47--55},
     publisher = {mathdoc},
     volume = {27},
     number = {11},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_11_a3/}
}
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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/