Error control for statistical solutions of hyperbolic systems of conservation laws
type: Item
instance of: scholarly article
title: Error control for statistical solutions of hyperbolic systems of conservation laws
zbMATH Open document ID: 1503.65227
author: Fabian Meyer
author: Ch. Rohde
author: Jan Giesselmann
published in: Calcolo
publication date: 2021-08-04T00:00:00Z
review text: The paper deals with hyperbolic systems of conservation laws and provides a reliable a posteriori error estimator, i.e., a computable upper bound for the numerical approximation error of dissipative statistical solutions is proposed in one spatial dimension. To this end, regularized empirical measures are used and the so-called relative entropy method by \textit{C. M. Dafermos} and \textit{R. J. DiPerna} [J. Differ. Equations 20, 90--114 (1976; Zbl 0323.35050)] can be applied. The error estimator is split into a stochastic and a spatiotemporal part. The Wasserstein distance between dissipative statistical solutions and the numerical approximation computed with a Runge-Kutta DG method in one spatial dimension is determined. Different numerical experiments illustrate the theoretical results, including a numerical approximation of the Wasserstein distance and an application to smooth and non-smooth solutions.
reviewed by: Kai Schneider
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 35Q31
zbMATH DE Number: 7378109
zbMATH Keywords: hyperbolic conservation laws
zbMATH Keywords: statistical solutions
zbMATH Keywords: a posteriori error estimates
zbMATH Keywords: discontinuous Galerkin method
Wikidata QID: Q115606194
describes a project that uses: POT
describes a project that uses: GitHub
MaRDI profile type: Publication
full work available at URL: s10092-021-00417-6
OpenAlex ID: W3158980235
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DOI: 10.1007/S10092-021-00417-6
description: scientific article; zbMATH DE number 7378109