A posteriori error estimation for a defect-correction method applied to convection-diffusion problems

We consider a two-point boundary-value problem for a singularly perturbed convection-diffusion problem. The problem is solved by using a defect-correction method based on a first-order upwind difference scheme and a second-order (unstabilized) central difference scheme. A robust a posteriori error estimate in the maximum norm is derived. It provides computable and guaranteed upper bounds for the discretization error. Numerical examples are given that illustrate the theoretical findings and verify the efficiency of the error estimator on a priori adapted meshes and in an adaptive mesh movement algorithm.