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A higher order, energy conserving discretization technique for beam dynamics simulations is presented. The method is based on the discontinuous Galerkin (DG) formulation. It utilizes locally refined, non-conforming grids which are designed for high spatial resolution along the path of charged particle beams. Apart from this formulation, the paper introduces a class of general symplectic integrators which conserve discrete energy in a modified sense. Specialized split-operator methods with optimum dispersion properties in the direction of particle motion are, additionally, derived. The application examples given in the paper are performed in a high performance computing environment. They include the self-consistent simulation of the RF electron gun developed by the Photo Injector Test Facility at DESY Zeuthen (PITZ) project and the computation of short range wake fields for ultra-relativistic electron bunches.