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

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

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 e...

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Hauptverfasser: Fjordholm, Ulrik Skre, Lye, Kjetil Olsen
Format: Artikel
Sprache:eng
Schlagworte:
Convergence rate
Hyperbolic conservation laws
Irregular data
Numerical methods
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Zusammenfassung: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.