A linearised singularly perturbed convection-diffusion problem with an interior layer

A linear time dependent singularly perturbed convection-diffusion problem is examined. The convective coefficient contains an interior layer (with a hyperbolic tangent profile), which in turn induces an interior layer in the solution. A numerical method consisting of a monotone finite difference operator and a piecewise-uniform Shishkin mesh is constructed and analysed. Neglecting logarithmic factors, first order parameter uniform convergence is established. (C) 2015 IMACS. Published by Elsevier B.V. All rights reserved.