Guaranteed high-precision estimation for P0 interpolation constants on triangular finite elements

Xuefeng Liu, Shin'Ichi Oishi

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


We consider an explicit estimation for error constants from two basic constant interpolations on triangular finite elements. The problem of estimating the interpolation constants is related to the eigenvalue problems of the Laplacian with certain boundary conditions. By adopting the Lehmann-Goerisch theorem and finite element spaces with a variable mesh size and polynomial degree, we succeed in bounding the leading eigenvalues of the Laplacian and the error constants with high precision. An online demo for the constant estimation is also available at

Original languageEnglish
Pages (from-to)635-652
Number of pages18
JournalJapan Journal of Industrial and Applied Mathematics
Issue number3
Publication statusPublished - 2013 Nov


  • Eigenvalue problem
  • Finite element method
  • Interpolation error constants
  • Lehmann-Goerisch theorem
  • hp-FEM

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics


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