A MUSCL method satisfying all the numerical entropy inequalities

Bouchut, F.; Bourdarias, Ch.; Perthame, B.

doi:10.1090/S0025-5718-96-00752-1

A MUSCL method satisfying all the numerical entropy inequalities
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by F. Bouchut, Ch. Bourdarias and B. Perthame PDF

Math. Comp. 65 (1996), 1439-1461 Request permission

Abstract:

We consider here second-order finite 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 $\Delta x^{1/2}$. It is obtained by a theory of second-order entropic projections involving values at the nodes of the grid and a variant of error estimates, which also gives new results for the first-order Engquist-Osher scheme.

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