Advertisement

\(H^3\) and \(H^4\) Regularities of the Poisson Equation on Polygonal Domains

  • Takehiko Kinoshita
  • Yoshitaka WatanabeEmail author
  • Mitsuhiro T. Nakao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)

Abstract

This paper presents two equalities of \(H^3\) and \(H^4\) 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.

Keywords

Poisson equation A priori estimates 

Notes

Acknowledgments

This work was supported by the Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (Nos. 15H03637, 15K05012) and supported by Program for Leading Graduate Schools “Training Program of Leaders for Integrated Medical System for Fruitful Healthy-Longevity Society.”

References

  1. 1.
    Grisvard, P.: Elliptic Problems in Nonsmooth Domains. Pitman, Boston (1985)zbMATHGoogle Scholar
  2. 2.
    Hell, T., Ostermann, A., Sandbichler, M.: Modification of dimension-splitting methods - overcoming the order reduction due to corner singularities. IMA J. Numer. Anal. 35, 1078–1091 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Hell, T., Ostermann, A.: Compatibility conditions for dirichlet and neumann problems of poisson’s equation on a rectangle. J. Math. Anal. Appl. 420, 1005–1023 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Nakao, M.T., Yamamoto, N., Kimura, S.: On best constant in the optimal error stimates for the \(H_0^1\)-projection into piecewise polynomial spaces. J. Approx. Theor. 93, 491–500 (1998)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Takehiko Kinoshita
    • 1
    • 2
  • Yoshitaka Watanabe
    • 3
    • 4
    Email author
  • 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.CREST, Japan Science and Technology AgencyKawaguchi, SaitamaJapan
  5. 5.National Institute of Technology, Sasebo CollegeNagasakiJapan

Personalised recommendations