A singularly perturbed problem with two parameters in two dimensions on graded meshes

Mirjana Brdar; Helena Zarin; Ljiljana Teofanov

doi:10.1016/j.camwa.2016.09.021

A singularly perturbed problem with two parameters in two dimensions on graded meshes

Mirjana Brdar, Helena Zarin, Ljiljana Teofanov

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

12 Scopus citations

Abstract

A numerical approximation of a convection–reaction–diffusion problem by standard bilinear finite elements is considered. Using Duran–Lombardi and Duran–Shishkin type meshes we prove first order error estimates in an energy norm. Numerical examples confirm our theoretical results and show smaller errors compared to the well-known Shishkin mesh.

Original language	English (US)
Pages (from-to)	2582-2603
Number of pages	22
Journal	Computers and Mathematics with Applications
Volume	72
Issue number	10
DOIs	https://doi.org/10.1016/j.camwa.2016.09.021
State	Published - Nov 1 2016
Externally published	Yes

Bibliographical note

Funding Information:
The work was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia , Projects III44006 and 174030 .

Publisher Copyright:
© 2016 Elsevier Ltd

Keywords

Galerkin finite element method
Graded meshes
Singularly perturbed problem
Two small parameters

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AU - Zarin, Helena

AU - Teofanov, Ljiljana

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N2 - A numerical approximation of a convection–reaction–diffusion problem by standard bilinear finite elements is considered. Using Duran–Lombardi and Duran–Shishkin type meshes we prove first order error estimates in an energy norm. Numerical examples confirm our theoretical results and show smaller errors compared to the well-known Shishkin mesh.

AB - A numerical approximation of a convection–reaction–diffusion problem by standard bilinear finite elements is considered. Using Duran–Lombardi and Duran–Shishkin type meshes we prove first order error estimates in an energy norm. Numerical examples confirm our theoretical results and show smaller errors compared to the well-known Shishkin mesh.

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KW - Graded meshes

KW - Singularly perturbed problem

KW - Two small parameters

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A singularly perturbed problem with two parameters in two dimensions on graded meshes

Abstract

Bibliographical note

Keywords

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