Defect correction on Shishkin-type meshes (Q5934380)

The authors consider a defect-correction method that combines a first-order upwinded difference scheme with a second-order central difference scheme for a model singularly perturbed convection-diffusion problem in one dimension on a class of Shishkin-type meshes. They give the first general proof of uniform second-order convergence of this method. As a corollary they derive error bounds for the gradient approximation of the upwind scheme. They also give some numerical experiments to support their theoretical results.