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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2015, Volume 157, Book 2, Pages 55–67 (Mi uzku1306)  

This article is cited in 1 scientific paper (total in 1 paper)

Interpolation of the function of two variables with large gradients in the boundary layers

A. I. Zadorin

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Omsk, Russia

Abstract: The problem of interpolation for the function of two variables with large gradients in the boundary layers is investigated. It is suggested that the function can be represented as a sum of a regular component with bounded derivatives up to some order and of two boundary layer components. The boundary layer components are known, but their coefficients are uncertain. Such representation is typical for the solution of a singular perturbed elliptic problem. A two-dimensional interpolation formula, which is exact on the boundary layer components, is deduced. The formula has the arbitrary number of nodes in each direction. The accuracy estimate, which is uniform in gradients of the interpolated function in the boundary layers, is proved. The results of numerical experiments are provided.

Keywords: function of two variables, large gradients, boundary layer component, non-polynomial interpolation, error estimation.

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UDC: 519.65
Received: 28.04.2015

Citation: A. I. Zadorin, “Interpolation of the function of two variables with large gradients in the boundary layers”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 157, no. 2, Kazan University, Kazan, 2015, 55–67

Citation in format AMSBIB
\Bibitem{Zad15}
\by A.~I.~Zadorin
\paper Interpolation of the function of two variables with large gradients in the boundary layers
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2015
\vol 157
\issue 2
\pages 55--67
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1306}
\elib{https://elibrary.ru/item.asp?id=23819777}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Zadorin, N. A. Zadorin, “Polinomialnaya interpolyatsiya funktsii dvukh peremennykh s bolshimi gradientami v pogranichnykh sloyakh”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 158, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2016, 40–50  mathnet  elib
  • Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
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