Enriched Spectral Method for Stiff Convection-Dominated Equations

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Abstract

A novel and simple numerical method for stiff convection-dominated problems is studied in presence of boundary or interior layers. A version of the spectral Chevyshev-collocation method enriched with the so-called corrector functions is investigated. The corrector functions here are designed to capture the stiffness of the layers (see the Appendix), and the proposed method does not rely on the adaptive grid points. The extensive numerical results demonstrate that the enriched spectral methods are very accurate with low computational cost.

Keywords

Spectral methods Enriched methods Boundary layers Convection–diffusion equations Collocation methods 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper. After this paper was completed, we learned during an AMS Sectional meeting in Bloomington, Indiana, of the work of [43]. The authors resolved the singularities of the mixed Dirichlet–Neumann boundary value problems using a version of enriched spectral methods. However, the way of enrichment is not similar since different types of singularities are considered here. Chang-Yeol Jung was supported by the National Research Foundation of Korea grant funded by the Ministry of Education (2015R1D1A1A01059837).

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics, and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA
  2. 2.Department of Mathematical Sciences, School of Natural ScienceUlsan National Institute of Science and TechnologyUlsanRepublic of Korea

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