Richardson Extrapolation for Linearly Degenerate Discontinuities
  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. 
J. W. Banks and T. D. Aslam
math.NA