Exponentially graded mesh for a singularly perturbed problem with two small parameters

Helena Zarin

doi:10.1016/j.apnum.2017.06.003

Exponentially graded mesh for a singularly perturbed problem with two small parameters

Helena Zarin

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

24 Scopus citations

Abstract

A one-dimensional singularly perturbed boundary value problem with two small perturbation parameters is numerically solved on an exponentially graded mesh. Using an h-version of the standard Galerkin method with higher order polynomials, we prove a robust convergence in the corresponding energy norm. Numerical experiments support theoretical findings.

Original language	English (US)
Pages (from-to)	233-242
Number of pages	10
Journal	Applied Numerical Mathematics
Volume	120
DOIs	https://doi.org/10.1016/j.apnum.2017.06.003
State	Published - Oct 2017
Externally published	Yes

Bibliographical note

Funding Information:
Research of this author is supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia under grant 174030.

Publisher Copyright:
© 2017 IMACS

Keywords

Exponentially graded mesh
Galerkin finite element method
Singularly perturbed problem
Two small parameters

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10.1016/j.apnum.2017.06.003

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title = "Exponentially graded mesh for a singularly perturbed problem with two small parameters",

abstract = "A one-dimensional singularly perturbed boundary value problem with two small perturbation parameters is numerically solved on an exponentially graded mesh. Using an h-version of the standard Galerkin method with higher order polynomials, we prove a robust convergence in the corresponding energy norm. Numerical experiments support theoretical findings.",

keywords = "Exponentially graded mesh, Galerkin finite element method, Singularly perturbed problem, Two small parameters",

author = "Helena Zarin",

note = "Funding Information: Research of this author is supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia under grant 174030. Publisher Copyright: {\textcopyright} 2017 IMACS",

year = "2017",

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doi = "10.1016/j.apnum.2017.06.003",

language = "English (US)",

volume = "120",

pages = "233--242",

journal = "Applied Numerical Mathematics",

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T1 - Exponentially graded mesh for a singularly perturbed problem with two small parameters

AU - Zarin, Helena

N1 - Funding Information: Research of this author is supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia under grant 174030. Publisher Copyright: © 2017 IMACS

PY - 2017/10

Y1 - 2017/10

N2 - A one-dimensional singularly perturbed boundary value problem with two small perturbation parameters is numerically solved on an exponentially graded mesh. Using an h-version of the standard Galerkin method with higher order polynomials, we prove a robust convergence in the corresponding energy norm. Numerical experiments support theoretical findings.

AB - A one-dimensional singularly perturbed boundary value problem with two small perturbation parameters is numerically solved on an exponentially graded mesh. Using an h-version of the standard Galerkin method with higher order polynomials, we prove a robust convergence in the corresponding energy norm. Numerical experiments support theoretical findings.

KW - Exponentially graded mesh

KW - Galerkin finite element method

KW - Singularly perturbed problem

KW - Two small parameters

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JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Exponentially graded mesh for a singularly perturbed problem with two small parameters

Abstract

Bibliographical note

Keywords

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