Space-time discontinuous Galerkin method for nonlinear water waves

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    A space–time discontinuous Galerkin (DG) finite element method for nonlinear water waves in an inviscid and incompressible fluid is presented. The space–time DG method results in a conservative numerical discretization on time dependent deforming meshes which follow the free surface evolution. The algorithm is higher order accurate, both in space and time, and closely related to an arbitrary Lagrangian Eulerian (ALE) approach. A detailed derivation of the numerical algorithm is given including an efficient procedure to solve the nonlinear algebraic equations resulting from the space–time discretization. Numerical examples are shown on a series of model problems to demonstrate the accuracy and capabilities of the method.
    Original languageUndefined
    Article number10.1016/
    Pages (from-to)17-39
    Number of pages23
    JournalJournal of computational physics
    Issue number2/1
    Publication statusPublished - 20 May 2007


    • METIS-242055
    • IR-63961
    • EWI-9462
    • MSC-65M60

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