On the practical accuracy of shock-capturing schemes

The paper suggests a method which allows to estimate the accuracy of translation of the Rankine–Hugoniot’s conditions through the shock wave front. The method concerns the calculation of the order of integral convergence of difference solution (as opposed to using its absolute value as in the norm $L_1$) on the intervals crossing the shock. In such integration the error arising in front of the shock due to its smearing, can be compensated by the similar error of the opposite sign after the front. Provided examples demonstrate that this approach allows to obtain the second order of integral convergence on the intervals crossing the shock for some of the classical high-order difference schemes.