Solution Decompositions for Linear Convection-Diffusion Problems

Abstract

We consider a singularly perturbed convection-diffusion problem. The existence of certain decompositions of the solution into a regular solution component and a layer component is studied. Such decompositions are useful for the convergence analysis of numerical methods. Our aim is to show that such decompositions exist under less restrictive assumptions on the data of the problem than those required in earlier publications.