Numerical Solution of a Singularly Perturbed Problem on a Circular Domain

Numerical Solution of a Singularly Perturbed Problem on a Circular Domain

We consider a singularly perturbed elliptic problem, of convection-diffusion type, posed on a circular domain. Using polar coordinates, simple upwinding and a piecewise-uniform Shishkin mesh in the radial direction, we construct a numerical method that is monotone, pointwise accurate and parameter-un...

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Bibliographic Details
Main Authors: A. F. Hegarty, E. O’Riordan
Format: Article
Language:English
Published: Yaroslavl State University 2016-06-01
Series:Modelirovanie i Analiz Informacionnyh Sistem
Subjects:
circular domain
convection-diffusion
parameter-uniform
shishkin mesh
Online Access:https://www.mais-journal.ru/jour/article/view/349
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spelling doaj-66fd416bb4a847dd9177536e5ee04af02021-07-29T08:15:21ZengYaroslavl State UniversityModelirovanie i Analiz Informacionnyh Sistem1818-10152313-54172016-06-0123334935610.18255/1818-1015-2016-3-349-356306Numerical Solution of a Singularly Perturbed Problem on a Circular DomainA. F. Hegarty0E. O’Riordan1University of Limerick, IrelandDublin City University, IrelandWe consider a singularly perturbed elliptic problem, of convection-diffusion type, posed on a circular domain. Using polar coordinates, simple upwinding and a piecewise-uniform Shishkin mesh in the radial direction, we construct a numerical method that is monotone, pointwise accurate and parameter-uniform under certain compatibility constraints. Numerical results are presented to illustrate the performance of the numerical method when these constraints are not imposed on the data.https://www.mais-journal.ru/jour/article/view/349circular domainconvection-diffusionparameter-uniformshishkin mesh
collection DOAJ
language English
format Article
sources DOAJ
author A. F. Hegarty
E. O’Riordan
spellingShingle A. F. Hegarty
E. O’Riordan
Numerical Solution of a Singularly Perturbed Problem on a Circular Domain
Modelirovanie i Analiz Informacionnyh Sistem
circular domain
convection-diffusion
parameter-uniform
shishkin mesh
author_facet A. F. Hegarty
E. O’Riordan
author_sort A. F. Hegarty
title Numerical Solution of a Singularly Perturbed Problem on a Circular Domain
title_short Numerical Solution of a Singularly Perturbed Problem on a Circular Domain
title_full Numerical Solution of a Singularly Perturbed Problem on a Circular Domain
title_fullStr Numerical Solution of a Singularly Perturbed Problem on a Circular Domain
title_full_unstemmed Numerical Solution of a Singularly Perturbed Problem on a Circular Domain
title_sort numerical solution of a singularly perturbed problem on a circular domain
publisher Yaroslavl State University
series Modelirovanie i Analiz Informacionnyh Sistem
issn 1818-1015
2313-5417
publishDate 2016-06-01
description We consider a singularly perturbed elliptic problem, of convection-diffusion type, posed on a circular domain. Using polar coordinates, simple upwinding and a piecewise-uniform Shishkin mesh in the radial direction, we construct a numerical method that is monotone, pointwise accurate and parameter-uniform under certain compatibility constraints. Numerical results are presented to illustrate the performance of the numerical method when these constraints are not imposed on the data.
topic circular domain
convection-diffusion
parameter-uniform
shishkin mesh
url https://www.mais-journal.ru/jour/article/view/349
work_keys_str_mv AT afhegarty numericalsolutionofasingularlyperturbedproblemonacirculardomain
AT eoriordan numericalsolutionofasingularlyperturbedproblemonacirculardomain
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