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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 4, Pages 79–87 (Mi vuu403)  

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

MATHEMATICS

Error of interpolation by sixth-degree polynomials on a triangle

N. V. Latypova

Department of Mathematical Analysis, Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: The paper considers Birkhoff-type triangle-based interpolation to a two-variable function by sixth-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 estimates from below are valid for any nondegenerate triangle.

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

Full text: PDF file (187 kB)
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UDC: 517.518
MSC: 41A05
Received: 19.10.2013

Citation: N. V. Latypova, “Error of interpolation by sixth-degree polynomials on a triangle”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 4, 79–87

Citation in format AMSBIB
\Bibitem{Lat13}
\by N.~V.~Latypova
\paper Error of interpolation by sixth-degree polynomials on a~triangle
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2013
\issue 4
\pages 79--87
\mathnet{http://mi.mathnet.ru/vuu403}


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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. V. Seliverstov, “Kubicheskie formy bez monomov ot dvukh peremennykh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:1 (2015), 71–77  mathnet  elib
    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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