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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.
O'Riordan, E. & Quinn, J. (2014) A linearised singularly perturbed convection-diffusion problem with an interior layer, Applied Numerical Mathematics Dec.