A MUSCL METHOD SATISFYING ALL THE NUMERICAL ENTROPY INEQUALITIES

We consider here second-order finite volume methods for one-dimensiona l scalar conservation laws. We give a method to determine a slope reco nstruction satisfying all the exact numerical entropy inequalities. It avoids inhomogeneous slope limitations and, at least, gives a converg ence rate of Delta x(1/2). It is obtained by a theory of second-order entropic projections involving values at the nodes of the grid and a v ariant of error estimates, which also gives new results for the first- order Engquist-Osher scheme.