Ht. Fan, EXISTENCE AND UNIQUENESS OF TRAVELING WAVES AND ERROR-ESTIMATES FOR GODUNOV SCHEMES OF CONSERVATION-LAWS, Mathematics of computation, 67(221), 1998, pp. 87-109
The existence and uniqueness of the Lipschitz continuous traveling wav
e of Godunov's scheme for scalar conservation laws are proved. The str
ucture of the traveling waves is studied. The approximation error of G
odunov's scheme on single shock solutions is shown to be O(1)Delta x.