Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations

Y. Xu, Chi-Wang Shu

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    66 Citations (Scopus)

    Abstract

    In this paper, we provide $L^2$ error estimates for the semi-discrete local discontinuous Galerkin methods for nonlinear convection-diffusion equations and KdV equations with smooth solutions. The main technical difficulty is the control of the inter-element jump terms which arise because of the nonlinearity of the PDEs and the discontinuous nature of the numerical method.
    Original languageUndefined
    Article number10.1016/j.cma.2006.10.043
    Pages (from-to)3805-3822
    Number of pages18
    JournalComputer methods in applied mechanics and engineering
    Volume196
    Issue number2/37-40
    DOIs
    Publication statusPublished - 1 Aug 2007

    Keywords

    • Nonlinear convection–diffusion equation
    • KdV equation
    • EWI-9464
    • MSC-65M15
    • MSC-65M60
    • METIS-242056
    • Error estimate
    • Local discontinuous Galerkin method
    • IR-63963

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