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Convergence rates of monotone schemes for conservation laws for data with unbounded total variation (2010.07642v1)
Published 15 Oct 2020 in math.NA and cs.NA
Abstract: We prove convergence rates of monotone schemes for conservation laws for H\"older continuous initial data with unbounded total variation, provided that the H\"older exponent of the initial data is greater than $1/2$. For strictly $\mathrm{Lip}+$ stable monotone schemes, we prove convergence for any positive H\"older exponent. Numerical experiments are presented which verify the theory.
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