SDFEM for an elliptic singularly perturbed problem with two parameters

Lj Teofanov; M. Brdar; S. Franz; H. Zarin

doi:10.1007/s10092-018-0293-0

SDFEM for an elliptic singularly perturbed problem with two parameters

Lj Teofanov, M. Brdar, S. Franz, H. Zarin

Mathematics

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8 Scopus citations

Abstract

A singularly perturbed problem with two small parameters in two dimensions is investigated. Using its discretization by a streamline-diffusion finite element method with piecewise bilinear elements on a Shishkin mesh, we analyze the superconvergence property of the method and suggest the choice of stabilization parameters to attain optimal error estimate in the corresponding streamline-diffusion norm. Numerical tests confirm our theoretical results.

Original language	English (US)
Article number	50
Journal	Calcolo
Volume	55
Issue number	4
DOIs	https://doi.org/10.1007/s10092-018-0293-0
State	Published - Dec 1 2018

Bibliographical note

Funding Information:
This paper was written during a visit by Mirjana Brdar to the Technical University of Dresden in December 2017–February 2018 supported by DAAD Grant No. 57314019. The work was also partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, Projects III44006 and 174030.

Publisher Copyright:
© 2018, Istituto di Informatica e Telematica del Consiglio Nazionale delle Ricerche.

Keywords

Singularly perturbed problem
Stabilization parameter
Streamline-diffusion method
Superconvergence
Two small parameters

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title = "SDFEM for an elliptic singularly perturbed problem with two parameters",

abstract = "A singularly perturbed problem with two small parameters in two dimensions is investigated. Using its discretization by a streamline-diffusion finite element method with piecewise bilinear elements on a Shishkin mesh, we analyze the superconvergence property of the method and suggest the choice of stabilization parameters to attain optimal error estimate in the corresponding streamline-diffusion norm. Numerical tests confirm our theoretical results.",

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T1 - SDFEM for an elliptic singularly perturbed problem with two parameters

AU - Teofanov, Lj

AU - Brdar, M.

AU - Franz, S.

AU - Zarin, H.

N1 - Funding Information: This paper was written during a visit by Mirjana Brdar to the Technical University of Dresden in December 2017–February 2018 supported by DAAD Grant No. 57314019. The work was also partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, Projects III44006 and 174030. Publisher Copyright: © 2018, Istituto di Informatica e Telematica del Consiglio Nazionale delle Ricerche.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - A singularly perturbed problem with two small parameters in two dimensions is investigated. Using its discretization by a streamline-diffusion finite element method with piecewise bilinear elements on a Shishkin mesh, we analyze the superconvergence property of the method and suggest the choice of stabilization parameters to attain optimal error estimate in the corresponding streamline-diffusion norm. Numerical tests confirm our theoretical results.

AB - A singularly perturbed problem with two small parameters in two dimensions is investigated. Using its discretization by a streamline-diffusion finite element method with piecewise bilinear elements on a Shishkin mesh, we analyze the superconvergence property of the method and suggest the choice of stabilization parameters to attain optimal error estimate in the corresponding streamline-diffusion norm. Numerical tests confirm our theoretical results.

KW - Singularly perturbed problem

KW - Stabilization parameter

KW - Streamline-diffusion method

KW - Superconvergence

KW - Two small parameters

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ER -

SDFEM for an elliptic singularly perturbed problem with two parameters

Abstract

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Keywords

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