Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains

Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper presents two expressions for H3 and H4 semi-norms for the solutions of the Poisson equation in two-dimensional polygonal domains. These equalities enable us to obtain higher order constructive a priori error estimates for finite element approximation of the Poisson equation with validated computing.

Original languageEnglish
Pages (from-to)629-636
Number of pages8
JournalJapan Journal of Industrial and Applied Mathematics
Volume33
Issue number3
DOIs
Publication statusPublished - 2016 Dec 1
Externally publishedYes

Fingerprint

Regular Solution
Poisson equation
A Priori Estimates
Poisson's equation
A Priori Error Estimates
Seminorm
Finite Element Approximation
Equality
Higher Order
Computing

Keywords

  • A priori estimates
  • Poisson equation

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

Cite this

Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains. / Kinoshita, Takehiko; Watanabe, Yoshitaka; Yamamoto, Nobito; Nakao, Mitsuhiro T.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 33, No. 3, 01.12.2016, p. 629-636.

Research output: Contribution to journalArticle

Kinoshita, Takehiko ; Watanabe, Yoshitaka ; Yamamoto, Nobito ; Nakao, Mitsuhiro T. / Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains. In: Japan Journal of Industrial and Applied Mathematics. 2016 ; Vol. 33, No. 3. pp. 629-636.
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