A technique to prove parameter-uniform convergence for a singularly perturbed convection–diffusion equation

A priori parameter explicit bounds on the solution of singularly perturbed elliptic problems of convection–diffusion type are established. Regular exponential boundary layers can appear in the solution. These bounds on the solutions and its derivatives are obtained using a suitable decomposition of the solution into regular and layer components. By introducing extensions of the coefficients to a larger domain, artificial compatibility conditions are not imposed in the derivation of these decompositions.