H3 and H4 regularities of the poisson equation on polygonal domains

Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents two equalities of H3 and H4 semi-norms for the solutions of the Poisson equation in a two-dimensional polygonal domain. 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
Title of host publicationMathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers
PublisherSpringer Verlag
Pages199-201
Number of pages3
Volume9582
ISBN (Print)9783319328584
DOIs
Publication statusPublished - 2016
Externally publishedYes
Event6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015 - Berlin, Germany
Duration: 2015 Nov 112015 Nov 13

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9582
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015
CountryGermany
CityBerlin
Period15/11/1115/11/13

Fingerprint

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

Keywords

  • A priori estimates
  • Poisson equation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Kinoshita, T., Watanabe, Y., & Nakao, M. T. (2016). H3 and H4 regularities of the poisson equation on polygonal domains. In Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers (Vol. 9582, pp. 199-201). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9582). Springer Verlag. https://doi.org/10.1007/978-3-319-32859-1_16

H3 and H4 regularities of the poisson equation on polygonal domains. / Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.

Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. Vol. 9582 Springer Verlag, 2016. p. 199-201 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9582).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kinoshita, T, Watanabe, Y & Nakao, MT 2016, H3 and H4 regularities of the poisson equation on polygonal domains. in Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. vol. 9582, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9582, Springer Verlag, pp. 199-201, 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015, Berlin, Germany, 15/11/11. https://doi.org/10.1007/978-3-319-32859-1_16
Kinoshita T, Watanabe Y, Nakao MT. H3 and H4 regularities of the poisson equation on polygonal domains. In Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. Vol. 9582. Springer Verlag. 2016. p. 199-201. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-32859-1_16
Kinoshita, Takehiko ; Watanabe, Yoshitaka ; Nakao, Mitsuhiro T. / H3 and H4 regularities of the poisson equation on polygonal domains. Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. Vol. 9582 Springer Verlag, 2016. pp. 199-201 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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