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arXiv · 2402.09814

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

Lourenço Beirão da Veiga·Daniele A. Di Pietro·Kirubell B. Haile
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Abstract

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.

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Lourenço Beirão da Veiga, Daniele A. Di Pietro, Kirubell B. Haile. 2024-02-15. A P\'eclet-robust discontinuous Galerkin method for nonlinear diffusion with advection. https://arxiv.org/abs/2402.09814

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