A P\'eclet-robust discontinuous Galerkin method for nonlinear diffusion with advection

We analyze a Discontinuous Galerkin method for a problem with linear advection-reaction and p-type diffusion, with Sobolev indices p (1, ). The discretization of the diffusion term is based on the full gradient including jump liftings and interior-penalty stabilization while, for the advective contribution, we consider a strengthened version of the classical upwind scheme. The developed error estimates track the dependence of the local contributions to the error on local P\'eclet numbers. A set of numerical tests supports the theoretical derivations.