Error estimation for discontinuous Galerkin solutions of two-dimensional hyperbolic problems
type: Item
instance of: scholarly article
title: Error estimation for discontinuous Galerkin solutions of two-dimensional hyperbolic problems
zbMATH Open document ID: 1020.65062
DOI: 10.1023/A:1022894504834
author: Lilia Krivodonova
author: J. E. Flaherty
published in: Advances in Computational Mathematics
publication date: 2003-05-04T00:00:00Z
review text: Discontinuous Galerkin discretization of conservation laws in two dimensions by means of piecewise polynomials on unstructured meshes are considered. The applied concept for deriving an asymptotically exact error estimation rests on a local superconvergence at the outflow ends of the triangular elements. The authors give detailed proofs for the obtained error expansions and evaluate approximately the discretization error by the leading terms of its series representations. The related coefficients can be obtained via simple linear systems. Finally two numerical examples are given which show an excellent coincidence between theoretical estimates and practically occurring errors.
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 1903989
zbMATH Keywords: discontinuous Galerkin method
zbMATH Keywords: error estimate
zbMATH Keywords: hyperbolic problem
zbMATH Keywords: superconvergence
zbMATH Keywords: conservation laws
zbMATH Keywords: numerical examples
reviewed by: Christian Grossmann
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1903989