  In this paper we investigate the use of Richardson extrapolation to estimate
the convergence rates for numerical solutions to advection problems involving
discontinuities. We use modified equation analysis to describe the expectation
of the approach. In general, the results do not agree with a-priori estimates
of the convergence rates. However, we identify one particular use case where
Richardson extrapolation does yield the proper result. We then demonstrate this
result using a number of numerical examples.
