# Determination of the Babuska-Aziz constar for the linear triangular finite element

Fumio Kikuchi, Xuefeng Liu

Research output: Contribution to journalArticle

15 Citations (Scopus)

### 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 equation t + tan t = 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.

Original language English 75-82 8 Japan Journal of Industrial and Applied Mathematics 23 1 Published - 2006 Feb

### Fingerprint

Error analysis
Triangular
Finite Element
Numerical Verification
A Posteriori Error Estimation
Interpolation Error
Transcendental
Error Estimation
Interpolation

### Keywords

• Babuska-Aziz constant
• Interpolation error estimation
• Linear triangular finite element

### ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics

### Cite this

Determination of the Babuska-Aziz constar for the linear triangular finite element. / Kikuchi, Fumio; Liu, Xuefeng.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 23, No. 1, 02.2006, p. 75-82.

Research output: Contribution to journalArticle

title = "Determination of the Babuska-Aziz constar for the linear triangular finite element",
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 equation t + tan t = 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.",
keywords = "Babuska-Aziz constant, Interpolation error estimation, Linear triangular finite element",
author = "Fumio Kikuchi and Xuefeng Liu",
year = "2006",
month = "2",
language = "English",
volume = "23",
pages = "75--82",
journal = "Japan Journal of Industrial and Applied Mathematics",
issn = "0916-7005",
publisher = "Springer Japan",
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AU - Kikuchi, Fumio

AU - Liu, Xuefeng

PY - 2006/2

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N2 - 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 t + tan t = 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.

AB - 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 t + tan t = 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.

KW - Babuska-Aziz constant

KW - Interpolation error estimation

KW - Linear triangular finite element

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