### 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 |
---|---|

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 |
---|---|

Country | Greece |

City | Rethymno, Crete |

Period | 09/9/18 → 09/9/22 |

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

## Fingerprint Dive into the research topics of 'On verified computations of the optimal constant in the a priori error estimates for h0 2-projection'. Together they form a unique fingerprint.

## 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