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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, Issue 3, Pages 53–64 (Mi vuu336)  

This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Independence of interpolation error estimates by fifth-degree polynomials on angles in a triangle

N. V. Latypova

Department of Mathematical Analysis, Udmurt State University, Izhevsk, Russia

Abstract: The paper considers several methods of Birkhoff-type triangle-based interpolation of two-variable function by fifth-degree polynomials. Similar estimates are automatically transferred to error estimates of related finite element method. The error estimates for the given elements depend only on the decomposition diameter, and do not depend on triangulation angles. We show that the estimates obtained are unimprovable. Unimprovability is understood in a following sense: there exists function from the given class and there exist absolute positive constants independent of triangulation such that for any nondegenerate triangle estimates from below are valid.

Keywords: error of interpolation, piecewise polynomial function, triangulation, finite element method.

Full text: PDF file (181 kB)
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UDC: 517.518
MSC: 41A05
Received: 29.03.2012

Citation: N. V. Latypova, “Independence of interpolation error estimates by fifth-degree polynomials on angles in a triangle”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 3, 53–64

Citation in format AMSBIB
\Bibitem{Lat12}
\by N.~V.~Latypova
\paper Independence of interpolation error estimates by fifth-degree polynomials on angles in a~triangle
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2012
\issue 3
\pages 53--64
\mathnet{http://mi.mathnet.ru/vuu336}


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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. N. V. Latypova, “Pogreshnost interpolyatsii mnogochlenami shestoi stepeni na treugolnike”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 4, 79–87  mathnet
    2. V. S. Bazhenov, N. V. Latypova, “Nezavisimost otsenok pogreshnosti interpolyatsii mnogochlenami stepeni $2k+1$ ot uglov treugolnika”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:2 (2016), 160–168  mathnet  crossref  mathscinet  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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