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SDFEM for an elliptic singularly perturbed problem with two parameters

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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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Authors and Affiliations

  1. Department for Fundamental Disciplines, Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, Novi Sad, 21000, Serbia

    Lj. Teofanov

  2. Faculty of Technology, University of Novi Sad, Novi Sad, 21000, Serbia

    M. Brdar

  3. Institute of Scientific Computing, Technical University of Dresden, 01062, Dresden, Germany

    S. Franz

  4. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Novi Sad, 21000, Serbia

    H. Zarin

Authors
  1. Lj. Teofanov
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  2. M. Brdar
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  3. S. Franz
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  4. H. Zarin
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Corresponding author

Correspondence to Lj. Teofanov.

Additional 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.

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Teofanov, L., Brdar, M., Franz, S. et al. SDFEM for an elliptic singularly perturbed problem with two parameters. Calcolo 55, 50 (2018). https://doi.org/10.1007/s10092-018-0293-0

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  • DOI: https://doi.org/10.1007/s10092-018-0293-0

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