Estimation of interpolation error constants for the triangular finite element

Fumio Kikuchi, Xuefeng Liu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We give some fundamental results on the error constants for the piecewise constant interpolation function and the piecewise linear one over triangles. We obtain explicit relotions for the dependence of such error constants on the geometric parameters of triangles. In particular, we explicitly determine the Babuska-Aziz constant, which plays an essential role in the interpolation error estimation of the linear triangular finite element The equation for determination is the transcendental equation √λ+tan √λ = 0, so that the solution can be numerically obtained with desired accuracy and verification. Such highly accurate approximate values for the constant as well as estimates for other constants can be widely used for a priori and a posteriori error estimations in adaptive computation and numerical verification of finite element solutions. .

Original languageEnglish
Title of host publication3rd International Conference on Computing, Communications and Control Technologies, CCCT 2005, Proceedings
PublisherInternational Institute of Informatics and Systemics, IIIS
Pages107-112
Number of pages6
Volume1
ISBN (Print)9806560469, 9789806560468
Publication statusPublished - 2005
Event3rd International Conference on Computing, Communications and Control Technologies, CCCT 2005 - Austin, TX
Duration: 2005 Jul 242005 Jul 27

Other

Other3rd International Conference on Computing, Communications and Control Technologies, CCCT 2005
CityAustin, TX
Period05/7/2405/7/27

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Keywords

  • Babuška-Aziz constant
  • Error estimates
  • FEM
  • Interpolation error constants.
  • Triangular element

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Control and Systems Engineering

Cite this

Kikuchi, F., & Liu, X. (2005). Estimation of interpolation error constants for the triangular finite element. In 3rd International Conference on Computing, Communications and Control Technologies, CCCT 2005, Proceedings (Vol. 1, pp. 107-112). International Institute of Informatics and Systemics, IIIS.