On graded meshes for a two-parameter singularly perturbed problem

Mirjana Brdar; Helena Zarin

doi:10.1016/j.amc.2016.01.060

On graded meshes for a two-parameter singularly perturbed problem

Mirjana Brdar, Helena Zarin

Research output: Contribution to journal › Review article › peer-review

16 Scopus citations

Abstract

A one-dimensional reaction-diffusion-convection problem is numerically solved by a finite element method on two layer-adapted meshes, Duran-type mesh and Duran-Shishkin-type mesh, both defined by recursive formulae. Robust error estimates in the energy norm are proved. Numerical results are given to illustrate the parameter-uniform convergence of numerical approximations.

Original language	English (US)
Pages (from-to)	97-107
Number of pages	11
Journal	Applied Mathematics and Computation
Volume	282
DOIs	https://doi.org/10.1016/j.amc.2016.01.060
State	Published - May 5 2016
Externally published	Yes

Bibliographical note

Funding Information:
The work has been supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia , Projects 174030 and III44006 . The authors would like to thank the anonymous reviewers for their valuable comments and suggestions which improved the quality of the paper.

Publisher Copyright:
© 2016 Elsevier Inc. All rights reserved.

Keywords

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

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10.1016/j.amc.2016.01.060

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title = "On graded meshes for a two-parameter singularly perturbed problem",

abstract = "A one-dimensional reaction-diffusion-convection problem is numerically solved by a finite element method on two layer-adapted meshes, Duran-type mesh and Duran-Shishkin-type mesh, both defined by recursive formulae. Robust error estimates in the energy norm are proved. Numerical results are given to illustrate the parameter-uniform convergence of numerical approximations.",

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author = "Mirjana Brdar and Helena Zarin",

note = "Funding Information: The work has been supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia , Projects 174030 and III44006 . The authors would like to thank the anonymous reviewers for their valuable comments and suggestions which improved the quality of the paper. Publisher Copyright: {\textcopyright} 2016 Elsevier Inc. All rights reserved.",

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T1 - On graded meshes for a two-parameter singularly perturbed problem

AU - Brdar, Mirjana

AU - Zarin, Helena

N1 - Funding Information: The work has been supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia , Projects 174030 and III44006 . The authors would like to thank the anonymous reviewers for their valuable comments and suggestions which improved the quality of the paper. Publisher Copyright: © 2016 Elsevier Inc. All rights reserved.

PY - 2016/5/5

Y1 - 2016/5/5

N2 - A one-dimensional reaction-diffusion-convection problem is numerically solved by a finite element method on two layer-adapted meshes, Duran-type mesh and Duran-Shishkin-type mesh, both defined by recursive formulae. Robust error estimates in the energy norm are proved. Numerical results are given to illustrate the parameter-uniform convergence of numerical approximations.

AB - A one-dimensional reaction-diffusion-convection problem is numerically solved by a finite element method on two layer-adapted meshes, Duran-type mesh and Duran-Shishkin-type mesh, both defined by recursive formulae. Robust error estimates in the energy norm are proved. Numerical results are given to illustrate the parameter-uniform convergence of numerical approximations.

KW - Galerkin finite element method

KW - Graded meshes

KW - Singularly perturbed problem

KW - Two small parameters

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U2 - 10.1016/j.amc.2016.01.060

DO - 10.1016/j.amc.2016.01.060

M3 - Review article

AN - SCOPUS:84959156267

SN - 0096-3003

VL - 282

SP - 97

EP - 107

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

On graded meshes for a two-parameter singularly perturbed problem

Abstract

Bibliographical note

Keywords

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