A posteriori error analysis for numerical approximations of Friedrichs systems
type: Item
instance of: scholarly article
title: A posteriori error analysis for numerical approximations of Friedrichs systems
zbMATH Open document ID: 0935.65096
author: Yanyan Li
published in: Numerische Mathematik
publication date: 2000-04-24T00:00:00Z
review text: An a posteriori error analysis for numerical approximations of Friedrichs systems is presented. The global error is decomposed into a locally created part and a propagating component. Residual-based two-sided local a posteriori error bounds are derived for the locally created part of the global error. These suggest taking the \(L^{2}\)-norm as well as weaker, dual norms of the computable residual as local error indicators. The dual graph norm of the residual \({\mathbf r}_{h}\) is further bounded from above and below in terms of the \(L^{2}\) norm of \(h{\mathbf r}_{h}\) where \(h\) is the local mesh size. The theoretical results are illustrated by a series of numerical experiments.
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 1356178
zbMATH Keywords: symmetric positive hyperbolic systems
zbMATH Keywords: energetic estimates
zbMATH Keywords: difference schemes
zbMATH Keywords: Friedrichs systems
zbMATH Keywords: a posteriori error bounds
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: s002110050426
OpenAlex ID: W2093687887
DOI: 10.1007/S002110050426
description: scientific article; zbMATH DE number 1356178