Long-time Asymptotic Behavior of Lax-Friedrichs Scheme (Journal of Partial Differential Equations, 1993)
In this paper we investigate the asymptotic stability of the discrete shocks of the Lax-Friedrichs scheme for hyperholic systems of conservation laws. For single equations, we show that the discrete shocks of the Lax-Friedrichs scheme are asymptotically stable in the sense of I&sup3 and I&sup1. For the systems of conservation laws, if the summation of initial perturbations equals to zero, we show the l&sup2 stability and l&sup1 boundedness.