### Abstract

In this paper, we show some constructive a priori error estimates for H_{0}
^{2}-projection into a space of polynomials on a one dimensional interval. Here, 'constructive' means we can get the error bounds in which all constants included are explicitly given or represented as a numerically computable form. By using the property of Legendre polynomials, we try to determine such constants as small as possible. Particularly, we will show the optimal constant could be enclosed in a very narrow interval. Then an application of the results to finite element H_{0}
^{2}- projection in one dimension is presented. This kind of estimates will play an important role in the numerical verification of solutions for nonlinear fourth order elliptic problems.

Original language | English |
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Title of host publication | Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 |

Pages | 926-929 |

Number of pages | 4 |

Volume | 1168 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

Event | International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 - Rethymno, Crete, Greece Duration: 2009 Sep 18 → 2009 Sep 22 |

### Other

Other | International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 |
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Country | Greece |

City | Rethymno, Crete |

Period | 09/9/18 → 09/9/22 |

### Fingerprint

### Keywords

- Constructive a priori error estimates
- Fourth order elliptic problem
- Legendre polynomials

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009*(Vol. 1168, pp. 926-929) https://doi.org/10.1063/1.3241634

**On verified computations of the optimal constant in the a priori error estimates for h0
2-projection.** / Nakao, Mitsuhiro T.; Kinoshita, Takehiko.

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

*Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009.*vol. 1168, pp. 926-929, International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009, Rethymno, Crete, Greece, 09/9/18. https://doi.org/10.1063/1.3241634

}

TY - GEN

T1 - On verified computations of the optimal constant in the a priori error estimates for h0 2-projection

AU - Nakao, Mitsuhiro T.

AU - Kinoshita, Takehiko

PY - 2009

Y1 - 2009

N2 - In this paper, we show some constructive a priori error estimates for H0 2-projection into a space of polynomials on a one dimensional interval. Here, 'constructive' means we can get the error bounds in which all constants included are explicitly given or represented as a numerically computable form. By using the property of Legendre polynomials, we try to determine such constants as small as possible. Particularly, we will show the optimal constant could be enclosed in a very narrow interval. Then an application of the results to finite element H0 2- projection in one dimension is presented. This kind of estimates will play an important role in the numerical verification of solutions for nonlinear fourth order elliptic problems.

AB - In this paper, we show some constructive a priori error estimates for H0 2-projection into a space of polynomials on a one dimensional interval. Here, 'constructive' means we can get the error bounds in which all constants included are explicitly given or represented as a numerically computable form. By using the property of Legendre polynomials, we try to determine such constants as small as possible. Particularly, we will show the optimal constant could be enclosed in a very narrow interval. Then an application of the results to finite element H0 2- projection in one dimension is presented. This kind of estimates will play an important role in the numerical verification of solutions for nonlinear fourth order elliptic problems.

KW - Constructive a priori error estimates

KW - Fourth order elliptic problem

KW - Legendre polynomials

UR - http://www.scopus.com/inward/record.url?scp=70450175229&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70450175229&partnerID=8YFLogxK

U2 - 10.1063/1.3241634

DO - 10.1063/1.3241634

M3 - Conference contribution

AN - SCOPUS:70450175229

SN - 9780735407091

VL - 1168

SP - 926

EP - 929

BT - Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009

ER -