Negative-order norm estimates for nonlinear hyperbolic conservation laws
type: Item
instance of: scholarly article
title: Negative-order norm estimates for nonlinear hyperbolic conservation laws
zbMATH Open document ID: 1266.65155
author: Liangyue Ji
author: Yan Xu
author: Jennifer K. Ryan
published in: Journal of Scientific Computing
publication date: 2013-04-08T00:00:00Z
review text: Negative-order norm estimates for the accuracy of discontinuous Galerkin (DG) approximations to scalar nonlinear hyperbolic equations with smooth solutions are established. For these special solutions, this ``hidden accuracy'' can be extracted through the use of a convolution kernel that is composed of a linear combination of B-splines. Previous investigations into extracting the superconvergence of DG methods using a convolution kernel have focused on linear hyperbolic equations. However, now it is demonstrated that it is possible to extend the smoothness-increasing accuracy-conserving filter for scalar nonlinear hyperbolic equations. Furthermore, theoretical error estimates are provided for the DG solutions that show an improvement to \((2k+m)\)-th order in the negative-order norm, where \(m\) depends upon the chosen flux.
reviewed by: Nina Shokina
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 6151379
zbMATH Keywords: discontinuous Galerkin method
zbMATH Keywords: nonlinear hyperbolic conservation laws
zbMATH Keywords: negative-order norm
zbMATH Keywords: SIAC filtering
zbMATH Keywords: post-processing
zbMATH Keywords: B-splines
zbMATH Keywords: superconvergence
zbMATH Keywords: smoothness-increasing accuracy-conserving filter
zbMATH Keywords: error estimates
MaRDI profile type: Publication
full work available at URL: s10915-012-9668-6
OpenAlex ID: W2112082878
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DOI: 10.1007/S10915-012-9668-6
description: scientific article; zbMATH DE number 6151379