An implicit discontinuous Galerkin finite element model for water waves

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    Abstract

    An overview is given of a discontinuous Galerkin finite element method for linear free surface water waves. The method uses an implicit time integration method which is unconditionally stable and does not suffer from the frequently encountered mesh dependent saw-tooth type instability at the free surface. The numerical discretization has minimal dissipation and small dispersion errors in the wave propagation. The algorithm is second order accurate in time and has an optimal rate of convergence O(hp+1) in the L2- norm, both in the potential and wave height, with p the polynomial order and h the mesh size. The numerical discretization is demonstrated with the simulation of water waves in a basin with a bump at the bottom.
    Original languageEnglish
    Title of host publicationComputational Mechanics
    Subtitle of host publicationProceedings of the Sixth World Congress on Computational Mechanics in conjunction with the Second Asian-Pacific Congress on Computational Mechanics, September 5-10, 2004, Beijing, China
    EditorsZ.H. Yao, M.W. Yuan, W.X. Zhong
    Place of PublicationBeijing
    PublisherTsinghua University Press
    Pages690-695
    Number of pages6
    ISBN (Print)9787302093435
    Publication statusPublished - 5 Sep 2004
    Event6th World Congress on Computational Mechanics, WCCM 2004 - Beijing, China
    Duration: 5 Sep 200410 Sep 2004
    Conference number: 6

    Conference

    Conference6th World Congress on Computational Mechanics, WCCM 2004
    Abbreviated titleWCCM VI
    CountryChina
    CityBeijing
    Period5/09/0410/09/04

    Keywords

    • Discontinuous Galerkin method
    • Water waves
    • Elliptic partial differential equations

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