SDFEM for an elliptic singularly perturbed problem with two parameters

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

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1 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 languageEnglish (US)
Article number50
JournalCalcolo
Volume55
Issue number4
DOIs
StatePublished - Dec 1 2018
Externally publishedYes

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.

Keywords

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

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