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Trudy Inst. Mat. i Mekh. UrO RAN, 2005, Volume 11, Number 2, Pages 120–130 (Mi timm194)  

This article is cited in 11 scientific papers (total in 11 papers)

A new cubic element in the FEM

Yu. N. Subbotin


Abstract: In the paper, a new two-dimensional cubic element in the finite element method is suggested. It is proved that, in contrast to the classical element with interpolation at the center of gravity, the new element under the approximation of any admissible derivatives is free of the known condition of “sine of the smallest angle” of triangulation. It proved well to replace this condition by a weaker condition of “sine of the greatest angle” of triangulation. It is established, up to absolute constants, that the obtained estimates of approximation errors of derivatives are unimprovable. For the new element, the estimates of approximation error become worse only for triangles with two small angles. In terms of barycentric coordinates, fundamental interpolating polynomials are explicitly written out for the suggested element.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2005, suppl. 2, S176–S187

Bibliographic databases:
UDC: 519.652.3
Received: 24.12.2004

Citation: Yu. N. Subbotin, “A new cubic element in the FEM”, Function theory, Trudy Inst. Mat. i Mekh. UrO RAN, 11, no. 2, 2005, 120–130; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S176–S187

Citation in format AMSBIB
\Bibitem{Sub05}
\by Yu.~N.~Subbotin
\paper A~new cubic element in the FEM
\inbook Function theory
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2005
\vol 11
\issue 2
\pages 120--130
\mathnet{http://mi.mathnet.ru/timm194}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200229}
\zmath{https://zbmath.org/?q=an:1126.65100}
\elib{http://elibrary.ru/item.asp?id=12040708}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2005
\issue , suppl. 2
\pages S176--S187


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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. N. V. Baidakova, “A method of Hermite interpolation by polynomials of the third degree on a triangle”, Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S49–S55  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. A. V. Meleshkina, “On the approximation of the derivatives of the Hermite interpolation polynomial on a triangle”, Comput. Math. Math. Phys., 50:2 (2010), 201–210  mathnet  crossref  mathscinet  adsnasa  isi
    5. 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
    6. 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
    7. N. V. Latypova, “Nezavisimost otsenok pogreshnosti interpolyatsii kubicheskimi mnogochlenami ot uglov treugolnika”, Tr. IMM UrO RAN, 17, no. 3, 2011, 233–241  mathnet  elib
    8. 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
    9. 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
    10. 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
    11. 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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