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

Research output: Contribution to journal › Article

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 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

Access to Document

10.1007/s13160-016-0223-y

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Kinoshita, T., Watanabe, Y., Yamamoto, N., & Nakao, M. T. (2016). Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains. Japan Journal of Industrial and Applied Mathematics, 33(3), 629-636. https://doi.org/10.1007/s13160-016-0223-y

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