An analysis of a defect-correction method for a model convection- diffusion equation. (English) Zbl 0672.65063

Ervin, V.; Layton, W.

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

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