A Singularly Perturbed Convection Diffusion Turning Point Problem with an Interior Layer

A linear singularly perturbed interior turning point problem with a continuous convection coefficient is examined in this paper. Parameter uniform numerical methods composed of monotone finite difference operators and piecewise-uniform Shishkin meshes, are constructed and analysed for this class of problems. A refined Shishkin mesh is placed around the location of the interior layer and we consider disrupting the centre point of this fine mesh away from the point where the convection coefficient is zero. Numerical results are presented to illustrate the theoretical parameter-uniform error bounds established.