A genuinely stable Lagrange–Galerkin scheme for convection-diffusion problems

Masahisa Tabata, Shinya Uchiumi

    Research output: Contribution to journal › Article

    3 Citations (Scopus)

    Abstract

    We present a Lagrange–Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange–Galerkin schemes may encounter the instability caused by numerical quadrature error, the present scheme is genuinely stable. For the (Formula presented.) -element we prove error estimates of (Formula presented.) in (Formula presented.) -norm and of (Formula presented.) in (Formula presented.) -norm. Numerical results reflect these estimates.

    Original languageEnglish
    Pages (from-to)121-143
    Number of pages23
    JournalJapan Journal of Industrial and Applied Mathematics
    Volume33
    Issue number1
    DOIs
    Publication statusPublished - 2016 Feb 1

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    Convection-diffusion Problems
    Numerical Quadrature
    Norm
    Error Estimates
    Convection
    Numerical Results
    Estimate

    Keywords

    • Convection-diffusion problems
    • Exact integration
    • Finite element method
    • Lagrange–Galerkin scheme

    ASJC Scopus subject areas

    • Applied Mathematics
    • Engineering(all)

    Cite this

    A genuinely stable Lagrange–Galerkin scheme for convection-diffusion problems. / Tabata, Masahisa; Uchiumi, Shinya.

    In: Japan Journal of Industrial and Applied Mathematics, Vol. 33, No. 1, 01.02.2016, p. 121-143.

    Research output: Contribution to journal › Article

    Tabata, M & Uchiumi, S 2016, 'A genuinely stable Lagrange–Galerkin scheme for convection-diffusion problems', Japan Journal of Industrial and Applied Mathematics, vol. 33, no. 1, pp. 121-143. https://doi.org/10.1007/s13160-015-0196-2
    Tabata M, Uchiumi S. A genuinely stable Lagrange–Galerkin scheme for convection-diffusion problems. Japan Journal of Industrial and Applied Mathematics. 2016 Feb 1;33(1):121-143. https://doi.org/10.1007/s13160-015-0196-2
    Tabata, Masahisa ; Uchiumi, Shinya. / A genuinely stable Lagrange–Galerkin scheme for convection-diffusion problems. In: Japan Journal of Industrial and Applied Mathematics. 2016 ; Vol. 33, No. 1. pp. 121-143.
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