A local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations

•A posteriori error analysis for a local method for elliptic PDEs.•Automatic local domain identification.•Efficiency in singularly perturbed regimes.•Error estimators based on flux reconstructions with weakened regularity. We introduce a local adaptive discontinuous Galerkin method for convection-di...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational physics 2022-02, Vol.451, p.110894, Article 110894
Main Authors: Abdulle, Assyr, Rosilho de Souza, Giacomo
Format: Article
Language:English
Subjects:
A posteriori error estimators
Adaptive algorithms
Computational physics
Convection
Diffusion
Discontinuous Galerkin
Elliptic equation
Galerkin method
Local scheme
Mathematical analysis
Reaction-diffusion equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:•A posteriori error analysis for a local method for elliptic PDEs.•Automatic local domain identification.•Efficiency in singularly perturbed regimes.•Error estimators based on flux reconstructions with weakened regularity. We introduce a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations. The proposed method is based on a coarse grid and iteratively improves the solution's accuracy by solving local elliptic problems in refined subdomains. For purely diffusion problems, we already proved that this scheme converges under minimal regularity assumptions (Abdulle and Rosilho de Souza, 2019) [1]. In this paper, we provide an algorithm for the automatic identification of the local elliptic problems' subdomains employing a flux reconstruction strategy. Reliable error estimators are derived for the local adaptive method. Numerical comparisons with a classical nonlocal adaptive algorithm illustrate the efficiency of the method.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2021.110894