Iterative solution of elliptic problems by approximate factorization
type: Item
instance of: scholarly article
title: Iterative solution of elliptic problems by approximate factorization
zbMATH Open document ID: 0889.65107
DOI: 10.1016/S0377-0427(97)00132-5
author: Eldar Giladi
author: Joseph B. Keller
published in: Journal of Computational and Applied Mathematics
publication date: 1998-01-28T00:00:00Z
review text: An iterative method for the numerical solution of singularly perturbed linear elliptic problems of second order is developed. The basis of the method is a defect correction iteration, but in the present work the operator, approximating the original differential one, is generated by a formal asymptotic factorization into two first-order operators. The resulting approximate operator is easily inverted numerically by solving a sequence of initial value problems. The algorithm combines the best of the asymptotic and the numerical approaches. It posseses a fast rate of convergence and is a stable one. Convergence analysis of both the continuous and the discrete iteration in one-dimensional case is presented. The scheme is also extended to a class of two-dimensional singularly perturbed elliptic problems. The method is demonstrated numerically on one- and two-dimensional model problems.
reviewed by: K.Zlateva
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 1100615
zbMATH Keywords: defect correction iteration
zbMATH Keywords: asymptotic factorization
zbMATH Keywords: preconditioners
zbMATH Keywords: singular perturbation
zbMATH Keywords: stability
zbMATH Keywords: convergence
MaRDI profile type: Publication
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full work available at URL: s0377-0427(97)00132-5
OpenAlex ID: W2047268894
description: scientific article; zbMATH DE number 1100615