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Determination of the Babuska-Aziz constant for the linear triangular finite element

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Abstract

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 equationt + tant = 0, so that the solution can be numerically obtained with desired accuracy and verification. Such highly accurate approximate values for the constant can be widely used for a priori and a posteriori error estimations in adaptive computation and/or numerical verification.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, 153-8914, Tokyo, Japan

    Fumio Kikuchi & Liu Xuefeng

Authors
  1. Fumio Kikuchi
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  2. Liu Xuefeng
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Kikuchi, F., Xuefeng, L. Determination of the Babuska-Aziz constant for the linear triangular finite element. Japan J. Indust. Appl. Math. 23, 75 (2006). https://doi.org/10.1007/BF03167499

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  • DOI: https://doi.org/10.1007/BF03167499

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