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

Mitsuhiro T. Nakao; Takehiko Kinoshita

doi:10.1063/1.3241634

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 proceeding › Conference 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 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	https://doi.org/10.1063/1.3241634
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

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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 proceeding › Conference 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

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10.1063/1.3241634