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

doi:10.1007/s13160-016-0223-y

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (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 language	English
Pages (from-to)	629-636
Number of pages	8
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	33
Issue number	3
DOIs	https://doi.org/10.1007/s13160-016-0223-y
Publication status	Published - 2016 Dec 1
Externally published	Yes

Keywords

A priori estimates
Poisson equation

ASJC Scopus subject areas

Engineering(all)
Applied Mathematics

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10.1007/s13160-016-0223-y

Cite this

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

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.",

keywords = "A priori estimates, Poisson equation",

author = "Takehiko Kinoshita and Yoshitaka Watanabe and Nobito Yamamoto and Nakao, {Mitsuhiro T.}",

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AU - Kinoshita, Takehiko

AU - Watanabe, Yoshitaka

AU - Yamamoto, Nobito

AU - Nakao, Mitsuhiro T.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

AB - 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.

KW - A priori estimates

KW - Poisson equation

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JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

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

Abstract

Keywords

ASJC Scopus subject areas

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