Multisymplectic Hamiltonian variational integrators

Variational integrators have traditionally been constructed from the perspective of Lagrangian mechanics, but there recent efforts to adopt discrete variational approaches symplectic discretization Hamiltonian mechanics using integrators. In this paper, we will extend these results setting multisymplectic field theories. We demonstrate that one can use notion Type II generating functionals for partial differential equations as basis systematically constructing Galerkin automatically satisfy a conservation law, and establish Noether's theorem discretizations are invariant under Lie group action on dual jet bundle. addition, spacetime tensor product discretizations, recover Bridges Reich, show theory Runge--Kutta is well-defined if only partitioned methods in space time.