A Péclet-robust discontinuous Galerkin method for nonlinear diffusion with advection

2024/02/15 by L. Beirão da Veiga, da Veiga, Lourenço Beirão, Daniele A. Di Pietro +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2402.09814

openalex publication_date 2024/02/15 · openalex created_date 2024/02/18 · openalex updated_date 2026/07/28

Abstract

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 Péclet numbers. A set of numerical tests supports the theoretical derivations.

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