2 research outputs found
Second-order convergence of monotone schemes for conservation laws
We prove that a class of monotone, \emph{-contractive} schemes for
scalar conservation laws converge at a rate of in the Wasserstein
distance (-distance), whenever the initial data is decreasing and consists
of a finite number of piecewise constants. It is shown that the
Lax--Friedrichs, Enquist--Osher and Godunov schemes are -contractive.
Numerical experiments are presented to illustrate the main result. To the best
of our knowledge, this is the first proof of second-order convergence of any
numerical method for discontinuous solutions of nonlinear conservation laws
Existence and uniqueness of traveling waves and error estimates for Godunov schemes of conservation laws
Abstract. The existence and uniqueness of the Lipschitz continuous traveling wave of Godunov’s scheme for scalar conservation laws are proved. The structure of the traveling waves is studied. The approximation error of Godunov’s scheme on single shock solutions is shown to be O(1)∆x. 1