Numerical approximation of solution derivatives of singularly peprturbed parabolic problems of convection-difffusion type

Abstract

Numerical approximations to the solution of a linear singularly perturbed parabolic convection-diffusion problem are generated using a backward Euler method in time and an upwinded finite difference operator in space on a piecewise-uniform Shishkin mesh. A proof is given to show first order convergence of these numerical approximations in an appropriately weighted C^1$-norm. Numerical results are given to illustrate the theoretical error bounds