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
Original Paper Area 2


This paper presents two expressions for \(H^3\) and \(H^4\) 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.


Poisson equation A priori estimates 

Mathematics Subject Classification

65G20 47F05 



The authors would like to thank Prof. Michael Plum and Dr. Kaori Nagatou for their advice and useful discussions. The authors heartily thank the two anonymous referees for their thorough reading and valuable comments. This work was supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 15K05012, 15H03637), the Program for Leading Graduate Schools “Training Program of Leaders for Integrated Medical System for Fruitful Healthy-Longevity Society,” and CREST, JST.


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Copyright information

© The JJIAM Publishing Committee and Springer Japan 2016

Authors and Affiliations

  • Takehiko Kinoshita
    • 1
    • 2
  • Yoshitaka Watanabe
    • 3
  • Nobito Yamamoto
    • 4
  • Mitsuhiro T. Nakao
    • 5
  1. 1.Center for the Promotion of Interdisciplinary Education and ResearchKyoto UniversityKyotoJapan
  2. 2.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  3. 3.Research Institute for Information TechnologyKyushu UniversityFukuokaJapan
  4. 4.Department of Communication Engineering and Informatics, Faculty of Informatics and EngineeringUniversity of Electro-CommunicationsTokyoJapan
  5. 5.Institute of Mathematics for IndustryKyushu UniversityNishi-kuJapan

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