RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 3, Pages 83–97 (Mi timm723)  

This article is cited in 8 scientific papers (total in 8 papers)

Influence of smoothness on the error of approximation of derivatives under local interpolation on triangulations

N. V. Baidakovaab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University

Abstract: The paper is concerned with one problem of function interpolation on a triangle. We consider a large class of interpolation conditions guaranteeing the smoothness of order $m$ of the resulting piecewise polynomial function on the triangulated domain. It is known that, for smoothness $m\ge1$, the known upper estimates for the error of approximation of derivatives of order $2$ and above by derivatives of interpolation polynomials defined on a triangulation element contain the sine of the smallest angle in the denominator. As a result, the “smallest angle condition” must be imposed on the triangulation. It was shown earlier that the influence of the smallest angle could be weakened (which does not mean that it can be eliminated in all cases). The principal aim of this paper is to show that, for a large number of methods of choosing interpolation conditions, including traditional conditions, the influence of the smallest angle of the triangle on the error of approximation of derivatives of a function by derivatives of the interpolation polynomial is essential for a number of derivatives of order $2$ and above for $m\ge1$. In the case $m=0$, the influence of the middle (largest) angle is important. As a consequence, the results on the unimprovability of the upper estimates obtained earlier are strengthened.

Keywords: multidimensional interpolation, finite element method, approximation.

Full text: PDF file (232 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2012, 277, suppl. 1, 33–47

Bibliographic databases:

UDC: 517.51
Received: 15.04.2011

Citation: N. V. Baidakova, “Influence of smoothness on the error of approximation of derivatives under local interpolation on triangulations”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 3, 2011, 83–97; Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 33–47

Citation in format AMSBIB
\Bibitem{Bai11}
\by N.~V.~Baidakova
\paper Influence of smoothness on the error of approximation of derivatives under local interpolation on triangulations
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 3
\pages 83--97
\mathnet{http://mi.mathnet.ru/timm723}
\elib{http://elibrary.ru/item.asp?id=17870123}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2012
\vol 277
\issue , suppl. 1
\pages 33--47
\crossref{https://doi.org/10.1134/S0081543812050057}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000305909000005}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84863604863}


Linking options:
  • http://mi.mathnet.ru/eng/timm723
  • http://mi.mathnet.ru/eng/timm/v17/i3/p83

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, “Otsenki sverkhu velichiny pogreshnosti approksimatsii proizvodnykh v konechnom elemente Sie–Klafa–Tochera”, Tr. IMM UrO RAN, 18, no. 4, 2012, 80–89  mathnet  elib
    2. N. V. Baidakova, “Novye otsenki velichin pogreshnosti approksimatsii proizvodnykh pri interpolyatsii funktsii mnogochlenami tretei stepeni na treugolnike”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 13:1(2) (2013), 15–19  mathnet  crossref  elib
    3. 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
    4. N. V. Baidakova, “A triangular finite element with new approximation properties”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 74–84  mathnet  crossref  mathscinet  isi  elib
    5. N. V. Baǐdakova, “On Jamet's estimates for the finite element method with interpolation at uniform nodes of a simplex”, Siberian Adv. Math., 28:1 (2018), 1–22  mathnet  crossref  crossref  elib
    6. A. A. Klyachin, “Postroenie triangulyatsii ploskikh oblastei metodom izmelcheniya”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 2(39), 18–28  mathnet  crossref
    7. N. V. Baidakova, “Lineinaya interpolyatsiya na tetraedre”, Tr. IMM UrO RAN, 24, no. 4, 2018, 80–84  mathnet  crossref  elib
    8. A. A. Klyachin, “Postroenie treugolnoi setki dlya oblastei, ogranichennykh zamknutymi prostymi krivymi”, Matematicheskaya fizika i kompyuternoe modelirovanie, 21:3 (2018), 31–38  mathnet  crossref
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Number of views:
    This page:262
    Full text:78
    References:23
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020