A P\'eclet-robust discontinuous Galerkin method for nonlinear diffusion with advection
<|reference_start|>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 $p\in (1, \infty)$. 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.<|reference_end|>
@article{da veiga2024a,
    title={A P\'eclet-robust discontinuous Galerkin method for nonlinear diffusion
  with advection},
    author={Lourenc{c}o Beir~ao da Veiga, Daniele A. Di Pietro, Kirubell B.
  Haile},
    journal={arXiv preprint arXiv:2402.09814},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.09814},
    primaryClass={math.NA cs.NA}
}