Abstract

This work is devoted to the study of singularly perturbed convection-diffusion equations in a channel domain when a nonlinear reaction term with polynomial growth is present. The authors find that the boundary layer structures are governed by certain simple recursive linear equations, and that this simplicity implies explicit point wise and norm estimates. They use the boundary layer structures in the finite element discretizations which leads to the stability in the approximating system and accurate approximation solutions with uniform mesh design.