Interior layers in a reaction-diffusion equation with a discontinuous diffusion coefficient

In this paper a problem arising in the modelling of semiconductor devices motivates the study of singularly perturbed differential equations of reaction–diffusion type with discontinuous data. The solutions of such problems typically contain interior layers where the gradient of the solution changes rapidly. Parameter–uniform methods based on piecewise–uniform Shishkin meshes are constructed and analysed for such problems. Numerical results are presented to support the theoretical results and to illustrate the benefits of using a piecewise–uniform Shishkin mesh over the use of uniform meshes in the simulation of a simple semiconductor device.