Singular perturbation of semi linear reaction-convection equations in a channel and numerical applications. (English) Zbl 1163.65053

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.


65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations