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Journal of Scientific Computing

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28-06-2019

The Optimal Convergence Rate of Monotone Schemes for Conservation Laws in the Wasserstein Distance

Authors: Adrian M. Ruf, Espen Sande, Susanne Solem

Published in: Journal of Scientific Computing | Issue 3/2019

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Abstract

In 1994, Nessyahu, Tadmor and Tassa studied convergence rates of monotone finite volume approximations of conservation laws. For compactly supported, \(\mathrm {Lip}^+\)-bounded initial data they showed a first-order convergence rate in the Wasserstein distance. Our main result is to prove that this rate is optimal. We further provide numerical evidence indicating that the rate in the case of \(\mathrm {Lip}^+\)-unbounded initial data is worse than first-order.

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Title: The Optimal Convergence Rate of Monotone Schemes for Conservation Laws in the Wasserstein Distance
Authors: Adrian M. Ruf
Espen Sande
Susanne Solem
Publication date: 28-06-2019
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2019
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-019-00996-1

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