In a recent work J. Sci. Comput. 16 (2001), 479-524,
B. Després and F. Lagoutière introduced a new approach to derive
numerical schemes for hyperbolic conservation laws. Its most
important feature is the ability to perform an exact resolution
for a single traveling discontinuity. However their scheme is not
entropy satisfying and can keep nonentropic discontinuities.
The purpose of our work is, starting from the previous one, to
introduce a new class of schemes for monotone scalar conservation laws,
that satisfy an entropy inequality,
while still resolving exactly the single traveling shocks or
contact discontinuities. We show that it is then possible to have
an excellent resolution of rarefaction waves, and also to avoid
the undesirable staircase effect. In practice, our numerical
experiments show second-order accuracy.
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