Abstract
The error in a defect-correction method for a model, one-dimensional convection-diffusion problem without turning points is analyzed. Although the analysis is limited to the one-dimensional problem, the scheme is a computationally attractive way to increase the accuracy in smooth regions of first-order schemes for general multidimensional problems.It is shown that in one dimension the kth approximation converges uniformly in $\varepsilon $ in regions bounded away from the layer with rate $O((\varepsilon _0 - \varepsilon )^k + h^2 )$, $\varepsilon _0 = O(h)$. The estimates degrade to $O(1)$ near layers. Numerical experiments confirm that this is precisely the behavior of the method.
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