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
Description
Summary: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.
ISSN:1818-1015
2313-5417

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