A space-time discontinuous Galerkin method for the elastic wave equation

In this work we present a new high order space-time discretization method based on a discontinuous Galerkin paradigm for the second order visco-elastodynamics equation. After introducing the method, we show that the resulting space-time discontinuous Galerkin formulation is well-posed, stable and retains optimal rate of convergence with respect to the discretization parameters, namely the mesh size and the polynomial approximation degree. A set of two and three-dimensional numerical experiments confirms the theoretical bounds.