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