Introduction

Abstract

Stationary linear reaction-convection-diffusion problems form the subject of this monograph:

$$ - \in u^ - bu^{'} + cu = f\text{ in (0,1), }u(0) = \gamma _0 ,\text{ }u(1) = \gamma _1 $$

and its two-dimensional analogue

$$ - \in \Delta u - b \cdot \nabla u + cu = f\text{ in }\Omega \subset \text{ }IR^2 \text{, }u|\partial \Omega = g$$

with a small positive parameter ε.

Such problems arise in various models of fluid flow [52,53,73]; they appear in the (linearised) Navier-Stokes and in the Oseen equations, in the equations modelling oil extraction from underground reservoirs [32], flows in chemical reactors [3] and convective heat transport with large Péclet number [56]. Other applications include the simulation of semiconductor devices [130].