On very accurate enclosure of the optimal constant in the a priori error estimates for H0 2-projection

Takehiko Kinoshita*, Mitsuhiro T. Nakao

*この研究の対応する著者

研究成果: Article査読

4 被引用数 (Scopus)

抄録

We present constructive a priori error estimates for H0 2-projection into a space of polynomials on a one-dimensional interval. Here, "constructive" indicates that we can obtain the error bounds in which all constants are explicitly given or are represented in a numerically computable form. Using the properties of Legendre polynomials, we consider a method by which to determine these constants to be as small as possible. Using the proposed technique, the optimal constant could be enclosed in a very narrow interval with result verification. Furthermore, constructive error estimates for finite element H0 2-projection in one dimension are presented. These types of estimates will play an important role in the numerical verification of solutions for nonlinear fourth-order elliptic problems as well as in the guaranteed a posteriori error analysis for the finite element method or the spectral method (e.g. Hashimoto et al. (2006) [2], Nakao et al. (2008) [3], Watanabe et al. (2009) [11]).

本文言語English
ページ(範囲)526-537
ページ数12
ジャーナルJournal of Computational and Applied Mathematics
234
2
DOI
出版ステータスPublished - 2010 5 15
外部発表はい

ASJC Scopus subject areas

  • 計算数学
  • 応用数学

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