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Convergence Rates of Monotone Schemes for Conservation Laws for Data with Unbounded Total Variation

Abstract

We prove convergence rates of monotone schemes for conservation laws for Hölder continuous initial data with unbounded total variation, provided that the Hölder exponent of the initial data is greater than 12/. For strictly Lip+ stable monotone schemes, we prove convergence for any positive Hölder exponent. Numerical experiments are presented which verify the theory.
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Category

Academic article

Language

English

Author(s)

Affiliation

  • SINTEF Digital / Mathematics and Cybernetics
  • University of Oslo

Year

2022

Published in

Journal of Scientific Computing

ISSN

0885-7474

Volume

91

View this publication at Norwegian Research Information Repository