Error expansion for a first-order upwind difference scheme applied to a model convection-diffusion problem

A singularly perturbed convection–diffusion problem isconsidered. The problem is discretized using a simple first-orderupwind difference scheme on general meshes. We derive an expansionof the error of the scheme that enables uniform error boundswith respect to the perturbation parameter in the discrete maximumnorm for both a defect correction method and the Richardsonextrapolation technique. This generalizes and simplifies resultsobtained in earlier publications by Fröhner et al.(2001,Numer. Algorithms, 26, 281–299) and by Natividad &Stynes (2003, Appl. Numer. Math., 45, 315–329). Numericalexperiments complement our theoretical results.