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Guaranteed high-precision estimation for P 0 interpolation constants on triangular finite elements

  • Xuefeng LiuEmail author
  • Shin’ichi Oishi
Original Paper Area 1

Abstract

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 http://www.xfliu.org/onlinelab/.

Keywords

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

Mathematics Subject Classification

35P15 65N30 65N25 65N15 

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Copyright information

© The JJIAM Publishing Committee and Springer Japan 2013

Authors and Affiliations

  1. 1.Research Institute for Science and EngineeringWaseda UniversityTokyoJapan
  2. 2.Faculty of Science and EngineeringWaseda UniversityTokyoJapan
  3. 3.CREST/JSTKawaguchiJapan

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