A note on iterative methods for solving singularly perturbed problems using non-monotone methods on Shishkin meshes

Ali R. Ansari; Alan F. Hegarty

doi:10.1016/S0045-7825(03)00369-4

A note on iterative methods for solving singularly perturbed problems using non-monotone methods on Shishkin meshes

Ali R. Ansari
, Alan F. Hegarty

University of Limerick

Research output: Contribution to journal › Article › peer-review

Abstract

Non-monotone methods with Shishkin meshes are employed in obtaining finite difference schemes for solving a linear two-dimensional steady state convection-diffusion problem. Preconditioners are used that significantly reduce the number of iterations of the linear solver. Computational results for a Galerkin method are presented which indicate parameter robust, super-linear orders of convergence.

Original language	English
Pages (from-to)	3673-3687
Number of pages	15
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	192
Issue number	33-34
DOIs	https://doi.org/10.1016/S0045-7825(03)00369-4
Publication status	Published - 15 Aug 2003

Keywords

Iterative solvers
Non-monotone methods
Preconditioning
Shishkin meshes

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10.1016/S0045-7825(03)00369-4

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title = "A note on iterative methods for solving singularly perturbed problems using non-monotone methods on Shishkin meshes",

abstract = "Non-monotone methods with Shishkin meshes are employed in obtaining finite difference schemes for solving a linear two-dimensional steady state convection-diffusion problem. Preconditioners are used that significantly reduce the number of iterations of the linear solver. Computational results for a Galerkin method are presented which indicate parameter robust, super-linear orders of convergence.",

keywords = "Iterative solvers, Non-monotone methods, Preconditioning, Shishkin meshes",

author = "Ansari, \{Ali R.\} and Hegarty, \{Alan F.\}",

year = "2003",

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T1 - A note on iterative methods for solving singularly perturbed problems using non-monotone methods on Shishkin meshes

AU - Ansari, Ali R.

AU - Hegarty, Alan F.

PY - 2003/8/15

Y1 - 2003/8/15

N2 - Non-monotone methods with Shishkin meshes are employed in obtaining finite difference schemes for solving a linear two-dimensional steady state convection-diffusion problem. Preconditioners are used that significantly reduce the number of iterations of the linear solver. Computational results for a Galerkin method are presented which indicate parameter robust, super-linear orders of convergence.

AB - Non-monotone methods with Shishkin meshes are employed in obtaining finite difference schemes for solving a linear two-dimensional steady state convection-diffusion problem. Preconditioners are used that significantly reduce the number of iterations of the linear solver. Computational results for a Galerkin method are presented which indicate parameter robust, super-linear orders of convergence.

KW - Iterative solvers

KW - Non-monotone methods

KW - Preconditioning

KW - Shishkin meshes

UR - https://www.scopus.com/pages/publications/0042887049

U2 - 10.1016/S0045-7825(03)00369-4

DO - 10.1016/S0045-7825(03)00369-4

M3 - Article

AN - SCOPUS:0042887049

SN - 0045-7825

VL - 192

SP - 3673

EP - 3687

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 33-34

ER -

A note on iterative methods for solving singularly perturbed problems using non-monotone methods on Shishkin meshes

Abstract

Keywords

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