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Sib. Èlektron. Mat. Izv., 2011, Volume 8, Pages 247–267 (Mi semr321)  

This article is cited in 5 scientific papers (total in 5 papers)

Interpolation of functions with the boundary layer components and its application in a two-grid method

A. I. Zadorina, N. A. Zadorinb

a Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science
b Omsk State University

Abstract: 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, nonpolynomial interpolation, elliptic problem, two-grid method.

Full text: PDF file (818 kB)
References: PDF file   HTML file
UDC: 519.632.4
MSC: 65N06
Received May 12, 2011, published September 7, 2011

Citation: A. I. Zadorin, N. A. Zadorin, “Interpolation of functions with the boundary layer components and its application in a two-grid method”, Sib. Èlektron. Mat. Izv., 8 (2011), 247–267

Citation in format AMSBIB
\Bibitem{ZadZad11}
\by A.~I.~Zadorin, N.~A.~Zadorin
\paper Interpolation of functions with the boundary layer components and its application in a two-grid method
\jour Sib. \`Elektron. Mat. Izv.
\yr 2011
\vol 8
\pages 247--267
\mathnet{http://mi.mathnet.ru/semr321}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Tikhovskaya, “Dvukhsetochnyi metod dlya ellipticheskogo uravneniya s pogranichnymi sloyami na setke Shishkina”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2012, 49–56  mathnet
    2. A. I. Zadorin, “Cubature formulas for a two-variable function with boundary-layer components”, Comput. Math. Math. Phys., 53:12 (2013), 1808–1818  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. S. V. Tikhovskaya, “Issledovanie dvukhsetochnogo metoda povyshennoi tochnosti dlya ellipticheskogo uravneniya reaktsii–diffuzii s pogranichnymi sloyami”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2015, 60–74  mathnet  elib
    4. A. I. Zadorin, “Interpolyatsiya funktsii dvukh peremennykh s bolshimi gradientami v pogranichnykh sloyakh”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 157, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2015, 55–67  mathnet  elib
    5. Zadorin A., “Two-Dimensional Interpolation of Functions With Large Gradients in Boundary Layers”, Numerical Analysis and Its Applications (NAA 2016), Lecture Notes in Computer Science, 10187, eds. Dimov I., Farago I., Vulkov L., Springer International Publishing Ag, 2017, 760–768  crossref  mathscinet  zmath  isi  scopus
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