Abstract
We 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. The method is shown to be convergent, uniformly in the diffusion parameter ε, of second order in the discrete maximum norm. As a corollary we derive error bounds for the gradient approximation of the upwind scheme. Numerical experiments support our theoretical results.
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Fröhner, A., Linß, T. & Roos, HG. Defect correction on Shishkin-type meshes. Numerical Algorithms 26, 281–299 (2001). https://doi.org/10.1023/A:1016664926018
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DOI: https://doi.org/10.1023/A:1016664926018