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Trudy Inst. Mat. i Mekh. UrO RAN, 2005, Volume 11, Number 2, Pages 47–52 (Mi timm188)  

This article is cited in 10 scientific papers (total in 10 papers)

A method of Hermite interpolation by polynomials of the third degree on a triangle

N. V. Baidakova


Abstract: As a rule, in constructing triangular finite elements of Hermite or Birkhoff type, the denominators of interpolation error bounds contain the sine of the minimum angle in the triangle. This leads to the necessity to impose some restrictions on the triangulation of the domain. Excluding the paper by Yu. N. Subbotin published in the present issue, the author does not know any description of the cases where the minimum angle is absent in the estimates of all derivatives up to order $n$ inclusive when a function is interpolated by Hermite or Birkhoff's polynomial of degree $n$. In this paper, a new method of Hermite interpolation of a function in two variables on a triangle by polynomials of degree 3 is suggested. For the proposed method, the sine of the minimum angle is absent in the denominators of error bounds for any derivatives of the function up to the third order, which makes it possible to weaken our requirements on the triangulation.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2005, suppl. 2, S49–S55

Bibliographic databases:
UDC: 519.652.3
Received: 27.12.2004

Citation: N. V. Baidakova, “A method of Hermite interpolation by polynomials of the third degree on a triangle”, Function theory, Trudy Inst. Mat. i Mekh. UrO RAN, 11, no. 2, 2005, 47–52; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S49–S55

Citation in format AMSBIB
\Bibitem{Bai05}
\by N.~V.~Baidakova
\paper A~method of Hermite interpolation by polynomials of the third degree on a~triangle
\inbook Function theory
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2005
\vol 11
\issue 2
\pages 47--52
\mathnet{http://mi.mathnet.ru/timm188}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200221}
\zmath{https://zbmath.org/?q=an:1141.41001}
\elib{http://elibrary.ru/item.asp?id=12040702}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2005
\issue , suppl. 2
\pages S49--S55


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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. Yu. N. Subbotin, “A new cubic element in the FEM”, Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S176–S187  mathnet  mathscinet  zmath  elib
    2. Yu. V. Matveeva, “Ob ermitovoi interpolyatsii mnogochlenami tretei stepeni na treugolnike s ispolzovaniem smeshannykh proizvodnykh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 7:1 (2007), 23–27  mathnet
    3. N. V. Baidakova, “On some interpolation third-degree polynomials on a three-dimensional simplex”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S44–S59  mathnet  crossref  isi  elib
    4. N. V. Latypova, “Nezavisimost otsenok pogreshnosti interpolyatsii mnogochlenami chetvertoi stepeni ot uglov treugolnika”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 3, 64–74  mathnet
    5. N. V. Baidakova, “Influence of smoothness on the error of approximation of derivatives under local interpolation on triangulations”, Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 33–47  mathnet  crossref  isi  elib
    6. N. V. Latypova, “Nezavisimost otsenok pogreshnosti interpolyatsii kubicheskimi mnogochlenami ot uglov treugolnika”, Tr. IMM UrO RAN, 17, no. 3, 2011, 233–241  mathnet  elib
    7. N. V. Latypova, “Nezavisimost otsenok pogreshnosti interpolyatsii mnogochlenami pyatoi stepeni ot uglov treugolnika”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 3, 53–64  mathnet
    8. N. V. Baidakova, “Otsenki sverkhu velichiny pogreshnosti approksimatsii proizvodnykh v konechnom elemente Sie–Klafa–Tochera”, Tr. IMM UrO RAN, 18, no. 4, 2012, 80–89  mathnet  elib
    9. N. V. Baidakova, “Lower estimates for the error of approximation of derivatives for composite finite elements with smoothness properties”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 29–39  mathnet  crossref  mathscinet  isi  elib
    10. 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
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