Convergence rates of monotone schemes for conservation laws for data with unbounded total variation

10/15/2020

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by   Ulrik Skre Fjordholm, et al.

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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 1/2. For strictly Lip^+ stable monotone schemes, we prove convergence for any positive Hölder exponent. Numerical experiments are presented which verify the theory.