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• W2617363427 abstract "In this paper, we prove necessary and sufficient conditions for a hybridizable discontinuous Galerkin (HDG) method to satisfy a multisymplectic conservation law, when applied to a canonical Hamiltonian system of partial differential equations. We show that these conditions are satisfied by the hybridized versions of several of the most commonly-used finite element methods, including mixed, nonconforming, and discontinuous Galerkin methods. (Interestingly, for the continuous Galerkin method in dimension greater than one, we show that multisymplecticity only holds in a weaker sense.) Consequently, these general-purpose finite element methods may be used for structure-preserving discretization (or semidiscretization) of canonical Hamiltonian systems of ODEs or PDEs. This establishes multisymplecticity for a large class of arbitrarily-high-order methods on unstructured meshes." @default.
• W2617363427 created "2017-06-05" @default.
• W2617363427 creator A5005515472 @default.
• W2617363427 creator A5064081913 @default.
• W2617363427 date "2019-04-22" @default.
• W2617363427 modified "2023-10-02" @default.
• W2617363427 title "Multisymplecticity of Hybridizable Discontinuous Galerkin Methods" @default.
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• W2617363427 doi "https://doi.org/10.1007/s10208-019-09415-1" @default.
• W2617363427 hasPublicationYear "2019" @default.
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