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.
richardson extrapolation regular boundary layer upwind scheme piecewise-uniform shishkin mesh singularly perturbed parabolic problem uniform convergence