A singularly perturbed model problem for numerical computation

In this note we introduce a model problem for the numerical solution of a two-dimensional singular perturbation problem. To combine a number of typical difficulties in a relatively simple problem, we propose to solve the linear convection-diffusion problem in the domain exterior of a circle. cribe the analytical solution of the problem and we comment on its numerical evaluation. For small values of the parameter, asymptotic approximations of the solution are given based on expansions by Friedlander (1958) and Waechter (1968). This information gives insight into the behaviour of the solution and allows the computation of a reference solution for small values of the parameter.