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On the numerical approximations of stiff convection–diffusion equations in a circle

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Abstract

Our aim in this article is to study the numerical solutions of singularly perturbed convection–diffusion problems in a circular domain and provide as well approximation schemes, error estimates and numerical simulations. To resolve the oscillations of classical numerical solutions due to the stiffness of our problem, we construct, via boundary layer analysis, the so-called boundary layer elements which absorb the boundary layer singularities. Using a \(P_1\) classical finite element space enriched with the boundary layer elements, we obtain an accurate numerical scheme in a quasi-uniform mesh.

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Authors and Affiliations

  1. Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, USA

    Youngjoon Hong & Roger Temam

  2. Department of Mathematical Sciences, School of Natural Science, Ulsan National Institute of Science and Technology, UNIST-gil 50, Ulsan, 689-798, Republic of Korea

    Chang-Yeol Jung

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  1. Youngjoon Hong
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  2. Chang-Yeol Jung
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  3. Roger Temam
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Correspondence to Youngjoon Hong.

Additional information

This work was supported in part by NSF Grants DMS 0906440 and DMS 1206438, and by the Research Fund of Indiana University and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2012R1A1B3001167).

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Hong, Y., Jung, CY. & Temam, R. On the numerical approximations of stiff convection–diffusion equations in a circle. Numer. Math. 127, 291–313 (2014). https://doi.org/10.1007/s00211-013-0585-x

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  • DOI: https://doi.org/10.1007/s00211-013-0585-x

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