Multisymplecticity of hybridizable discontinuous Galerkin methods (Q2291729)

Hamiltonian ODEs possess a symplectic flow, which has motivated the research on so called symplectic methods. Similarly, Hamiltonian PDEs satisfy a multisymplectic conservation law. Though the importance of such a property is not yet completely understood, the research on methods satisfying such a property is an active field of investigation. In this paper, the framework of the so called ``hybridizable discontinuous Galerkin (HDG) methods'' (see [\textit{Yu. S. Il'yashenko} and \textit{S. Yu. Yakovenko}, Russ. Math. Surv. 46, No. 1, 1--43 (1991; Zbl 0744.58006); translation from Usp. Mat. Nauk 46, No. 1(277), 3--39 (1991)]) is used to study the multisimplecticity of the finite element methods in this class. This establishes multisymplecticity for a large class of arbitrarily high-order methods on unstructured meshes.