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A Babuška-Aziz type proof of the circumradius condition

  • Kenta Kobayashi
  • Takuya TsuchiyaEmail author
Original Paper Area 2

Abstract

In this paper the error of polynomial interpolation of degree 1 on triangles is considered. The circumradius condition, which is more general than the maximum angle condition, is explained and proved by the technique given by Babuška-Aziz.

Keywords

Interpolation error Finite element methods The maximum angle condition The circumradius condition 

Mathematics Subject Classification (2000)

65D05 65N30 

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References

  1. 1.
    Babuška I., Aziz A.K.: On the angle condition in the finite element method. SIAM J. Numer. Anal 13, 214–226 (1976)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Ciarlet, P.G.: The finite element methods for elliptic problems, North Holland, 1978, reprint by SIAM 2008Google Scholar
  3. 3.
    Hannukainen A., Korotov S., Křížek M.: The maximum angle condition is not necessary for convergence of the finite element method. Numer. Math. 120, 79–88 (2011)CrossRefGoogle Scholar
  4. 4.
    Jamet P.: Estimations d’erreur pour des elements finis droits presque degeneres. R.A.I.R.O. Anal. Numer 10, 43–61 (1976)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Kobayashi K.: On the interpolation constants over triangular elements (in Japanese). RIMS Kokyuroku 1733, 58–77 (2011)Google Scholar
  6. 6.
    Kobayashi, K.: Remarkable upper bounds for the interpolation error constants on the triangles, in preparation Google Scholar
  7. 7.
    Kufner, A., John, O., Fučík, S.: Function spaces. Noordhoff International Publishing (1977)Google Scholar
  8. 8.
    Liu X., Kikuchi F.: Analysis and estimation of error constants for P 0 and P 1 interpolations over triangular finite elements. J. Math. Sci. Univ. Tokyo 17, 27–78 (2010)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Zlámal M.: On the finite element method. Numer. Math. 12, 394–409 (1968)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© The JJIAM Publishing Committee and Springer Japan 2013

Authors and Affiliations

  1. 1.Graduate School of Commerce and ManagementHitotsubashi UniversityKunitachiJapan
  2. 2.Graduate School of Science and EngineeringEhime UniversityMatsuyamaJapan

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