Monotone conservative finite-difference schemes satisfying discrete OSLC for uniformly convex flux conservation laws achieve the same two-sided 1/ε Kolmogorov entropy bounds as exact entropy solutions.
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Kolmogorov $\varepsilon$-entropy of numerical solutions for scalar conservation laws with convex flux
Monotone conservative finite-difference schemes satisfying discrete OSLC for uniformly convex flux conservation laws achieve the same two-sided 1/ε Kolmogorov entropy bounds as exact entropy solutions.