ABSTRACT
Mathematical models that involve a combination of convective and diffusive processes are among the most widespread in all of science, engineering and other fields where mathematical modelling is important. Very often the dimensionless parameter that measures the relative strength of the diffusion is quite small; so one often meets with situations where thin boundary and interior layers are present and singular perturbation problems arise. This chapter begin by collecting together some typical problems where the convection-diffusion phenomenon occurs. It considers some of the difficulties commonly experienced with numerical methods of approximation, and summarises the main approaches that will be taken to overcome them. The complete system of equations is probably one of the most complicated mathematical models in widespread use and it is clear that its character is dominated by several embedded convection-diffusion problems.
