Geodesic
Interpolation of functions with the boundary layer components and its application in a two-grid method
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 247-267

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As known, elliptic equation with regular boundary layers can be solved using difference scheme on an uniform mesh or on a mesh, dense in boundary layers. In both cases we have to solve a linear system of equations by iterations. We can reduce a number of iterations, if we preliminarily solve a problem on a coarse mesh. In this case we need to interpolate the mesh solution from a coarse mesh to a fine mesh. In a case of the uniform mesh we construct interpolations, fitted to the boundary layer components. We prove that in a case of Shishkin mesh the polynomial interpolation has the property of an uniform accuracy and may be used in a two-grid method.
Keywords: boundary layer, elliptic problem, two-grid method.
Mots-clés : nonpolynomial interpolation 
@article{SEMR_2011_8_a20,
     author = {A. I. Zadorin and N. A. Zadorin},
     title = {Interpolation of functions with the boundary layer components and its application in a two-grid method},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {247--267},
     publisher = {mathdoc},
     volume = {8},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2011_8_a20/}
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A. I. Zadorin; N. A. Zadorin. Interpolation of functions with the boundary layer components and its application in a two-grid method. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 247-267. http://geodesic.mathdoc.fr/item/SEMR_2011_8_a20/