Symplectic Hamiltonian finite element methods for linear elastodynamics

We present a class of high-order finite element methods that can conserve the linear and angular momenta as well energy for equations elastodynamics. These are devised by exploiting preserving Hamiltonian structure show several mixed element, discontinuous Galerkin, hybridizable Galerkin (HDG) belong to this class. discretize semidiscrete system in time using symplectic integrator order ensure properties resulting methods, which called methods. For particular HDG method, we obtain optimal error estimates present, numerical experiments confirm its orders convergence all variables conservation properties.