Semi-analytical numerical methods for convection-dominated problems with turning points

Chang Yeol Jung, Thien Binh Nguyen

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10 Citations (Scopus)

Abstract

In this article we aim to study finite volume approximations which approximate the solutions of convection-dominated problems possessing the so-called interior transition layers. The stiffness of such problems is due to a small parameter multiplied to the highest order derivative which introduces various transition layers at the boundaries and at the interior points where certain compatibility conditions do not meet. Here, we are interested in resolving interior transition layers at turning points. The proposed semi-analytic method features interior layer correctors which are obtained from singular perturbation analysis near the turning points. We demonstrate this method is efficient, stable and it shows 2nd-order convergence in the approximations.

Original languageEnglish
Pages (from-to)314-332
Number of pages19
JournalInternational Journal of Numerical Analysis and Modeling
Volume10
Issue number2
Publication statusPublished - 2013
Externally publishedYes

Keywords

  • Boundary layers
  • Compatibility conditions
  • Convection-diffusion equations
  • Finite volume methods
  • Singular perturbation analysis
  • Transition layers
  • Turning points

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