A Shock Indicator for Adaptive Schemes for Conservation Laws

In this paper we discuss an adaptive method for the compulation of discontinuous solutions of hyperbolic conservation laws. In each time level we use very simple sensors for detecting discontinuities of the solution. The adaptive scheme use first order upwind flux computation in the immediate neighborhood of these irregularities. Since the differential equation holds in the smoothness domain, we follow the characteristics in the lime marching procedure at grid points in that domain.