Methods and Applications of Analysis

Volume 10 (2003)

Number 4

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

Pages: 487 – 512

DOI: http://dx.doi.org/10.4310/MAA.2003.v10.n4.a1

Authors

NAN JIANG

HUANAN YANG

Abstract

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.

Full Text (PDF format)