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Numerische Mathematik

, Volume 127, Issue 2, pp 291–313 | Cite as

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

  • Youngjoon HongEmail author
  • Chang-Yeol Jung
  • Roger Temam
Article

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.

Mathematics Subject Classification

74S05 34D15 34E05 76E06 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute for Scientific Computing and Applied MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Department of Mathematical SciencesSchool of Natural Science, Ulsan National Institute of Science and TechnologyUlsanRepublic of Korea

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