Development and L2-analysis of a single-step characteristics finite difference scheme of second order in time for convection-diffusion problems

Hirofumi Notsu, Hongxing Rui, Masahisa Tabata

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    A new finite difference scheme based on the method of characteristics is presented for convection-diffusion problems. The scheme is of single-step and second order in time, and the matrix of the derived system of linear equations is symmetric. Since it is a finite difference scheme, we can get rid of numerical integration which may cause some instability in the characteristics finite element method. An optimal error estimate is proved in the framework of the discrete L2-theory. Numerical results are shown to recognize the convergence order and advantages of the scheme.

    Original languageEnglish
    Pages (from-to)343-380
    Number of pages38
    JournalJournal of Algorithms and Computational Technology
    Volume7
    Issue number3
    DOIs
    Publication statusPublished - 2013 Sep 1

    Fingerprint

    Convection-diffusion Problems
    Linear equations
    Finite Difference Scheme
    Finite element method
    Characteristics Method
    Convergence Order
    Method of Characteristics
    Optimal Error Estimates
    System of Linear Equations
    Numerical integration
    Finite Element Method
    Numerical Results
    Convection
    Framework

    Keywords

    • Discrete L-Analysis
    • Finite difference method
    • Second order in time
    • The method of characteristics

    ASJC Scopus subject areas

    • Numerical Analysis
    • Computational Mathematics
    • Applied Mathematics

    Cite this

    Development and L2-analysis of a single-step characteristics finite difference scheme of second order in time for convection-diffusion problems. / Notsu, Hirofumi; Rui, Hongxing; Tabata, Masahisa.

    In: Journal of Algorithms and Computational Technology, Vol. 7, No. 3, 01.09.2013, p. 343-380.

    Research output: Contribution to journalArticle

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