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We consider here second-order nite volume methods for one- dimensional scalar conservation laws. We give a method to determine a slope reconstruction satisfying all the exact numerical entropy inequalities. It avoids inhomogeneous slope limitations and, at least, gives a convergence rate of x1=2. It is obtained by a theory of second-order entropic projections involv- ing values at the nodes of the grid and a variant of error estimates, which also gives new results for the rst-order Engquist-Osher scheme.

A MUSCL method satisfying all the numerical entropy inequalities