A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media (Q556014)

The authors propose a discontinuous Galerkin schema for a symmetric hyperbolic system of first order. The coefficient matrices in this system related to the time and spatial derivatives are space dependent, but are assumed to be piecewise constant on a used polyhedral subdivision of the domain. For the underlying space-time discretization the authors apply a so called tent pitching algorithm that takes into account the form of the wave front. First, the proposed bilinear form is analyzed on single elements as well as on macroelements and the existence of a unique solution of the obtained discrete is proved. Further, an error estimate for the proposed discretization method is provided. Finally, for the acoustic wave equation the direct application of the method is discussed and some numerical results are given.