  A finite difference method is constructed for a singularly perturbed
convection diffusion problem posed on an annulus. The method involves combining
polar coordinates, an upwind finite difference operator and a piecewise-uniform
Shishkin mesh in the radial direction. Compatibility constraints are imposed on
the data in the vicinity of certain characteristic points to ensure that
interior layers do not form within the annulus. A theoretical parameter-uniform
error bound is established and numerical results are presented to illustrate
the performance of the numerical method applied to two particular test
problems.
