### 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 language | English |
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Title of host publication | 3rd International Conference on Computing, Communications and Control Technologies, CCCT 2005, Proceedings |

Publisher | International Institute of Informatics and Systemics, IIIS |

Pages | 107-112 |

Number of pages | 6 |

Volume | 1 |

ISBN (Print) | 9806560469, 9789806560468 |

Publication status | Published - 2005 |

Event | 3rd International Conference on Computing, Communications and Control Technologies, CCCT 2005 - Austin, TX Duration: 2005 Jul 24 → 2005 Jul 27 |

### Other

Other | 3rd International Conference on Computing, Communications and Control Technologies, CCCT 2005 |
---|---|

City | Austin, TX |

Period | 05/7/24 → 05/7/27 |

### Fingerprint

### 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

*3rd International Conference on Computing, Communications and Control Technologies, CCCT 2005, Proceedings*(Vol. 1, pp. 107-112). International Institute of Informatics and Systemics, IIIS.

**Estimation of interpolation error constants for the triangular finite element.** / Kikuchi, Fumio; Liu, Xuefeng.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*3rd International Conference on Computing, Communications and Control Technologies, CCCT 2005, Proceedings.*vol. 1, International Institute of Informatics and Systemics, IIIS, pp. 107-112, 3rd International Conference on Computing, Communications and Control Technologies, CCCT 2005, Austin, TX, 05/7/24.

}

TY - GEN

T1 - Estimation of interpolation error constants for the triangular finite element

AU - Kikuchi, Fumio

AU - Liu, Xuefeng

PY - 2005

Y1 - 2005

N2 - 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. .

AB - 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. .

KW - Babuška-Aziz constant

KW - Error estimates

KW - FEM

KW - Interpolation error constants.

KW - Triangular element

UR - http://www.scopus.com/inward/record.url?scp=84906973893&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84906973893&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9806560469

SN - 9789806560468

VL - 1

SP - 107

EP - 112

BT - 3rd International Conference on Computing, Communications and Control Technologies, CCCT 2005, Proceedings

PB - International Institute of Informatics and Systemics, IIIS

ER -