Discontinuous Hamiltonian finite element method for linear hyperbolic systems

Y. Xu, Jacobus J.W. van der Vegt, Onno Bokhove

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    Abstract

    We develop a Hamiltonian discontinuous finite element discretization of a generalized Hamiltonian system for linear hyperbolic systems, which include the rotating shallow water equations, the acoustic and Maxwell equations. These equations have a Hamiltonian structure with a bilinear Poisson bracket, and as a consequence the phase-space structure, “mass��? and energy are preserved. We discretize the bilinear Poisson bracket in each element with discontinuous elements and introduce numerical fluxes via integration by parts while preserving the skew-symmetry of the bracket. This automatically results in a mass and energy conservative discretization. When combined with a symplectic time integration method, energy is approximately conserved and shows no drift. For comparison, the discontinuous Galerkin method for this problem is also used. A variety numerical examples is shown to illustrate the accuracy and capability of the new method.
    Original languageUndefined
    Article number10.1007/s10915-008-9191-y
    Pages (from-to)241-265
    Number of pages25
    JournalJournal of scientific computing
    Volume35
    Issue numberWP 08-02/2-3
    DOIs
    Publication statusPublished - 2008

    Keywords

    • Rotating shallow water equations · Acoustic equations · Maxwell equations ·Hamiltonian dynamics · Discontinuous Galerkin method · Numerical flux
    • IR-65304
    • METIS-255124
    • EWI-14888

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