ON WAVEWISE ENTROPY INEQUALITIES FOR HIGH-RESOLUTION SCHEMES WITH SOURCE TERMS I: THE SEMI-DISCRETE CASE

We extend the framework and the convergence criteria of wavewise entropy inequalities of [H. Yang, Math. Comp., (1996), pp. 45-67] to a large class of semi-discrete high resolution schemes for hyperbolic conservation laws with source terms. This approach is based on an extended theory of Yang [22] on wave tracking and wave analysis and the theory of Vol'pert [21] on BV solutions. For the Cauchy problem of convex conservation laws with source terms, we use one of the criteria to prove the convergence to the entropy solution of generalized MUSCL schemes and a class of schemes using flux limiters previously discussed in 1984 by Sweby.

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Published 1 January 2003