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Numer. Anal."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>We prove that a class of monotone finite volume schemes for scalar conservation laws with discontinuous flux converge at a rate of sqrtDelta x in L^1, whenever the flux is strictly monotone in u and the spatial dependency of the flux is piecewise constant with finitely many discontinuities. We also present numerical experiments to illustrate the main result. To the best of our knowledge, this is the first proof of any type of convergence rate for numerical methods for conservation laws with discontinuous, nonlinear flux. Our proof relies on convergence rates for conservation laws with initial and boundary value data. 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