Richardson extrapolation technique for singularly perturbed parabolic convection-diffusion problems

This paper deals with the study of a post-processing technique for one-dimensional singularly perturbed parabolic convection-diffusion problems exhibiting a regular boundary layer. For discretizing the time derivative, we use the classical backward-Euler method and for the spatial discretization the simple upwind scheme is used on a piecewise-uniform Shishkin mesh. We show that the use of Richardson extrapolation technique improves the epsilon-uniform accuracy of simple upwinding in the discrete supremum norm from O (N (-1) ln N + Delta t) to O (N (-2) ln(2) N + Delta t (2)), where N is the number of mesh-intervals in the spatial direction and Delta t is the step size in the temporal direction. The theoretical result is also verified computationally by applying the proposed technique on two test examples.