Superconvergence of monotone difference schemes for piecewise smooth solutions of convex conservation laws

Abstract

In this paper we show that the monotone difference methods with smooth numerical fluxes possess superconvergence property when applied to strictly convex conservation laws with piecewise smooth solutions. More precisely, it is shown that not only the approximation solution converges to the entropy solution, its central difference also converges to the derivative of the entropy solution away from the shocks.