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

Xuefeng Liu, Shinichi Oishi

    Research output: Contribution to journal › Article

    6 Citations (Scopus)

    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/.

    Original languageEnglish
    Pages (from-to)635-652
    Number of pages18
    JournalJapan Journal of Industrial and Applied Mathematics
    Volume30
    Issue number3
    DOIs
    Publication statusPublished - 2013 Nov

    Fingerprint

    Triangular
    Interpolation
    Interpolate
    Finite Element
    Polynomials
    Boundary conditions
    Eigenvalue Problem
    Mesh
    Eigenvalue
    Polynomial
    Theorem

    Keywords

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

    ASJC Scopus subject areas

    • Applied Mathematics
    • Engineering(all)

    Cite this

    Guaranteed high-precision estimation for P0 interpolation constants on triangular finite elements. / Liu, Xuefeng; Oishi, Shinichi.

    In: Japan Journal of Industrial and Applied Mathematics, Vol. 30, No. 3, 11.2013, p. 635-652.

    Research output: Contribution to journal › Article

    Liu, X & Oishi, S 2013, 'Guaranteed high-precision estimation for P0 interpolation constants on triangular finite elements', Japan Journal of Industrial and Applied Mathematics, vol. 30, no. 3, pp. 635-652. https://doi.org/10.1007/s13160-013-0120-6
    Liu X, Oishi S. Guaranteed high-precision estimation for P0 interpolation constants on triangular finite elements. Japan Journal of Industrial and Applied Mathematics. 2013 Nov;30(3):635-652. https://doi.org/10.1007/s13160-013-0120-6
    Liu, Xuefeng ; Oishi, Shinichi. / Guaranteed high-precision estimation for P0 interpolation constants on triangular finite elements. In: Japan Journal of Industrial and Applied Mathematics. 2013 ; Vol. 30, No. 3. pp. 635-652.
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