High-order Discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes

We propose and analyze a high-order Discontinuous Galerkin Finite Element Method for the approximate solution of wave propagation problems modeled by the elastodynamics equations on computational meshes made by polygonal and polyhedral elements. We analyze the well posedness of the resulting formulation, prove hp-version error a-priori estimates, and present a dispersion analysis, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion properties. The theoretical estimates are confirmed through various two-dimensional numerical verifications.