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Journal of Scientific Computing

Erschienen in:

01.02.2013

Negative-Order Norm Estimates for Nonlinear Hyperbolic Conservation Laws

verfasst von: Liangyue Ji, Yan Xu, Jennifer K Ryan

Erschienen in: Journal of Scientific Computing | Ausgabe 2-3/2013

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Abstract

In this paper, we establish negative-order norm estimates for the accuracy of discontinuous Galerkin (DG) approximations to scalar nonlinear hyperbolic equations with smooth solutions. For these special solutions, we are able to extract this “hidden accuracy” 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, we now demonstrate that it is possible to extend the Smoothness-Increasing Accuracy-Conserving filter for scalar nonlinear hyperbolic equations. Furthermore, we provide theoretical error estimates for the DG solutions that show improvement to \((2k+m)\)-th order in the negative-order norm, where \(m\) depends upon the chosen flux.

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Titel: Negative-Order Norm Estimates for Nonlinear Hyperbolic Conservation Laws
verfasst von: Liangyue Ji
Yan Xu
Jennifer K Ryan
Publikationsdatum: 01.02.2013
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2-3/2013
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-012-9668-6

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