Singularly perturbed reaction-diffusion equations and finite element discretisations

Abstract:

In this lecture singularly perturbed linear reaction-diffusion problems in one and two dimensions are considered. These are elliptic equations that change character when the perturbation parameter tends to zero. As a result boundary and/or interior layers will form.

We give an introduction into the analysis of this kind of problems (stability and asymptotic structure of the layers). Then we move on to approximations by finite element methods. In particular we will discuss the suitability of certain energy-like norms for measuring convergence for this type of layer problems. A flavour of the style of convergence analysis will be given.