ON WAVEWISE ENTROPY INEQUALITY FOR HIGH-RESOLUTION SCHEMES II - FULLYDISCRETE MUSCL SCHEMES WITH EXACT EVOLUTION IN SMALL TIME

In this paper, we extend the framework and the convergence criteria of wavewise entropy inequality of [H. Yang, Math. Comp., 65 (1996), pp. 45-67] to fully discrete high resolution schemes satisfying certain TV D nonoscillatory conditions. For the Cauchy problem of convex conserva tion laws in one space dimension, we use one of the criteria to prove the convergence of the MUSCL scheme toward the entropy solution, assum ing that each time step of the scheme consists of a minmod slope limit er, an exact time evolution, and a standard cell averaging; the CFL nu mber is less than 0.5; and the initial condition is of bounded variati on.