Discontinuous Galerkin error estimation for linear symmetric hyperbolic systems

In this manuscript we present an error analysis for the discontinuous Galerkin discretization error of multi-dimensional first-order linear symmetric hyperbolic systems of partial differential equations. We perform a local error analysis by writing the local error as a series and showing that its leading term can be expressed as a linear combination of Legendre polynomials of degree p   and p+1p+1. We apply these asymptotic results and solve relatively small local problems to compute efficient and asymptotically exact estimates of the finite element error. We present computational results for several linear hyperbolic systems in one, two and three dimensions.