  In this work we construct reliable a posteriori estimates for some
discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic
conservation laws. We make use of appropriate reconstructions of the discrete
solution together with the relative entropy stability framework.
  The methodology we use is quite general and allows for a posteriori control
of discontinuous Galerkin schemes with standard flux choices which appear in
the approximation of conservation laws.
  In addition to the analysis, we conduct some numerical benchmarking to test
the robustness of the resultant estimator.
