Relative entropy based error estimates for discontinuous Galerkin schemes

These notes give an overview on how the relative entropy stability framework can be employed to derive a posteriori error estimates for semi-(spatially)-discrete discontinuous Galerkin schemes approximating systems of hyperbolic conservation laws endowed with one strictly convex entropy. We also show how these methods can be extended as to cover a related, higher order, model for compressible multiphase flows with non-convex energy.