AN ENTROPY SATISFYING MUSCL SCHEME
FOR
SYSTEMS OF CONSERVATION LAWS

    F.Coquel
    P.G. Le Floch

For the high order numerical approximation of  
hyperbolic systems of conservation laws, we 
propose to use as a building principle 
an entropy diminishing criterion 
instead of the familiar total variation diminishing 
criterion introduced by Harten for scalar equations. 
Based on this new criterion,
we derive entropy diminishing projections
that ensure, both, the second order of accuracy and 
all of the classical discrete entropy inequalities. 
The resulting scheme is a nonlinear version of 
the classical Van Leer's MUSCL scheme.

Strong convergence of this second order, entropy 
satisfying scheme is proved for systems of two equations. 
Numerical tests demonstrate the interest of our theory.

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