On the numerical approximations of stiff convection–diffusion equations in a circle

Abstract

Our aim in this article is to study the numerical solutions of singularly perturbed convection---diffusion problems in a circular domain and provide as well approximation schemes, error estimates and numerical simulations. To resolve the oscillations of classical numerical solutions due to the stiffness of our problem, we construct, via boundary layer analysis, the so-called boundary layer elements which absorb the boundary layer singularities. Using a $$P_1$$ P 1 classical finite element space enriched with the boundary layer elements, we obtain an accurate numerical scheme in a quasi-uniform mesh.