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

Mitsuhiro T. Nakao, Takehiko Kinoshita

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publicationNumerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009
Pages926-929
Number of pages4
Volume1168
DOIs
Publication statusPublished - 2009
Externally publishedYes
EventInternational Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009 - Rethymno, Crete, Greece
Duration: 2009 Sep 182009 Sep 22

Other

OtherInternational Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009
CountryGreece
CityRethymno, Crete
Period09/9/1809/9/22

Fingerprint

projection
estimates
intervals
Legendre functions
polynomials

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Nakao, M. T., & Kinoshita, T. (2009). On verified computations of the optimal constant in the a priori error estimates for h0 2-projection. In 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.

Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009. Vol. 1168 2009. p. 926-929.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nakao, MT & Kinoshita, T 2009, On verified computations of the optimal constant in the a priori error estimates for h0 2-projection. in 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
Nakao MT, Kinoshita T. On verified computations of the optimal constant in the a priori error estimates for h0 2-projection. In Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009. Vol. 1168. 2009. p. 926-929 https://doi.org/10.1063/1.3241634
Nakao, Mitsuhiro T. ; Kinoshita, Takehiko. / On verified computations of the optimal constant in the a priori error estimates for h0 2-projection. Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009. Vol. 1168 2009. pp. 926-929
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