Jh. Wang et G. Warnecke, ON ENTROPY CONSISTENCY OF LARGE TIME-STEP SCHEMES .2. APPROXIMATE RIEMANN SOLVERS, SIAM journal on numerical analysis, 30(5), 1993, pp. 1252-1267
It is shown that for scalar conservation laws with a convex flux funct
ion any sequence of approximate solutions, constructed by large time s
tep schemes using approximate Riemann solvers as a building block, giv
es the unique entropy solution in the limit of decreasing mesh size if
the Courant number is less than 1. When the curvature of the flux fun
ction is nearly constant the above results may be extended to Courant
numbers slightly larger than 1.