A shock indicator for adaptive schemes for conservation laws (Q1387757)

Second order difference expressions are applied to estimate the smoothness of a given function. The performance of these sensors is tested with scalar examples in one and two space dimensions. The authors apply the sensors to detect shocks in approximate solutions of conservation laws. Based on these shock indicators they propose a numerical method as follows: In regions where the solution appears to be smooth, the method of characteristics is applied. Otherwise, a conservative upwind method is used. Computational examples with Burger's and the Buckley-Leverett equation validate the numerical approach.