Numerical solution of a singularly perturbed problem on a circular domain

We consider a singularly perturbed elliptic problem, of convection-diffusion type, posed on a circular domain. Using polar coordinates, simple upwinding and a piecewise-uniform Shishkin mesh in the radial direction, we construct a numerical method that is monotone, pointwise accurate and parameter-uniform under certain compatibility constraints. Numerical results are presented to illustrate the performance of the numerical method when these constraints are not imposed on the data.