A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem

Helena Zarin; Hans Görg Roos; Ljiljana Teofanov

doi:10.1007/s40314-016-0339-3

A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem

Helena Zarin, Hans Görg Roos, Ljiljana Teofanov

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5 Scopus citations

Abstract

We propose a continuous interior penalty finite element method designed for a third-order singularly perturbed problem. Using higher order polynomials on Shishkin-type layer-adapted meshes, a robust convergence has been proved in the corresponding energy norm. Moreover, we show numerical experiments which support our theoretical findings.

Original language	English (US)
Pages (from-to)	175-190
Number of pages	16
Journal	Computational and Applied Mathematics
Volume	37
Issue number	1
DOIs	https://doi.org/10.1007/s40314-016-0339-3
State	Published - Mar 1 2018
Externally published	Yes

Bibliographical note

Funding Information:
The work of H. Zarin and the Lj. Teofanov was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia under Grant 174030.

Publisher Copyright:
© 2016, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.

Keywords

Interior penalty finite element method
Layer-adapted mesh
Singularly perturbed differential equation
Third-order boundary value problem

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abstract = "We propose a continuous interior penalty finite element method designed for a third-order singularly perturbed problem. Using higher order polynomials on Shishkin-type layer-adapted meshes, a robust convergence has been proved in the corresponding energy norm. Moreover, we show numerical experiments which support our theoretical findings.",

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note = "Funding Information: The work of H. Zarin and the Lj. Teofanov was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia under Grant 174030. Publisher Copyright: {\textcopyright} 2016, SBMAC - Sociedade Brasileira de Matem{\'a}tica Aplicada e Computacional.",

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doi = "10.1007/s40314-016-0339-3",

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AU - Zarin, Helena

AU - Roos, Hans Görg

AU - Teofanov, Ljiljana

N1 - Funding Information: The work of H. Zarin and the Lj. Teofanov was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia under Grant 174030. Publisher Copyright: © 2016, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - We propose a continuous interior penalty finite element method designed for a third-order singularly perturbed problem. Using higher order polynomials on Shishkin-type layer-adapted meshes, a robust convergence has been proved in the corresponding energy norm. Moreover, we show numerical experiments which support our theoretical findings.

AB - We propose a continuous interior penalty finite element method designed for a third-order singularly perturbed problem. Using higher order polynomials on Shishkin-type layer-adapted meshes, a robust convergence has been proved in the corresponding energy norm. Moreover, we show numerical experiments which support our theoretical findings.

KW - Interior penalty finite element method

KW - Layer-adapted mesh

KW - Singularly perturbed differential equation

KW - Third-order boundary value problem

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JF - Computational and Applied Mathematics

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A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem

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