  In this article we study the two dimensional singularly perturbed heat
equation in a circular domain. The aim is to develop a numerical method with a
uniform mesh, avoiding mesh refinement at the boundary thanks to the use of a
relatively simple representation of the boundary layer. We provide the
asymptotic expansion of the solution at first order and derive the boundary
layer element resulting from the boundary layer analysis. We then perform the
convergence analysis introducing the boundary layer element in the finite
element space thus obtaining what is called an "enriched Galerkin space".
Finally we present and comment on numerical simulations using a quasi-uniform
grid and the modified finite element method.
