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JSCIC
2008

Discontinuous Hamiltonian Finite Element Method for Linear Hyperbolic Systems

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Discontinuous Hamiltonian Finite Element Method for Linear Hyperbolic Systems
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. Keywords Rotating shallow water equa...
Yan Xu, Jaap J. W. van der Vegt, Onno Bokhove
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where JSCIC
Authors Yan Xu, Jaap J. W. van der Vegt, Onno Bokhove
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