Interior Layers in Singularly Perturbed Problems

To construct layer adapted meshes for a class of singularly perturbed problems, whose solutions contain boundary layers, it is necessary to identify both the location and the width of any boundary layers present in the solution. Additional interior layers can appear when the data for the problem is not sufficiently smooth. In the context of singularly perturbed partial differential equations, the presence of any interior layer typically requires the introduction of a transformation of the problem, which facilitates the necessary alignment of the mesh to the trajectory of the interior layer. Here we review a selection of published results on such problems to illustrate the variety of ways that interior layers can appear.