Richardson extrapolation for a convection–diffusion problem using a Shishkin mesh Original Research Article

We consider a convection–diffusion two-point boundary value problem on a piecewise-uniform Shishkin mesh, and show that when simple upwinding is used, a version of Richardson extrapolation improves the accuracy of the computed solution (measured in the discrete L∞ norm) from O(N−1lnN) to O(N−2ln2N), where N+1 mesh points are used. Numerical tests are provided to support these theoretical results.