Singular perturbation of semi-linear reaction-convection equations in a channel and numerical applications

Abstract

In this article, we investigate a way to analyze and approximate singularly perturbed convection-diffusion equations in a channel domain when a nonlinear reaction term with polynomial growth is present. We verify that the boundary layer structures are governed by certain simple recursive linear equations and this simplicity implies explicit pointwise and norm estimates. Furthermore, we can utilize the boundary layer structures (elements) in the finite elements discretizations which lead to the stability in the approximating systems and accurate approximation solutions with an economical mesh design, i.e., uniform mesh.