Ervin, V.; Layton, W. An analysis of a defect-correction method for a model convection- diffusion equation. (English) Zbl 0672.65063 SIAM J. Numer. Anal. 26, No. 1, 169-179 (1989). The paper derives sharp local error estimates for a defect-correction method applied to the one-dimensional model problem \(-\epsilon u''+f(x)u'+g(x)u=q(x),\) \(0<x<1\), \(f>0\), \(u(0)=\alpha\), \(u(1)=\beta\). The kth approximation is shown to converge uniformly in \(\epsilon\) in regions bounded away from the layer with rate \(O((\epsilon_ 0-\epsilon)^ k+h^ 2)\), \(\epsilon_ 0=O(h)\) while near the layers the estimate degrades to O(1). These theoretical estimates are supported by a numerical example. Reviewer: P.Onumanyi Cited in 26 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B05 Linear boundary value problems for ordinary differential equations 34E15 Singular perturbations, general theory for ordinary differential equations 76R99 Diffusion and convection Keywords:convection-diffusion equation; uniform convergence; local error estimates; defect-correction method; numerical example PDF BibTeX XML Cite \textit{V. Ervin} and \textit{W. Layton}, SIAM J. Numer. Anal. 26, No. 1, 169--179 (1989; Zbl 0672.65063) Full Text: DOI