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Two-Dimensional Interpolation of Functions with Large Gradients in Boundary Layers

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10187)

Abstract

Question of two-dimensional interpolation of functions with large gradients in the boundary layers is considered. The problem is that an application of polynomial interpolation on an uniform mesh to functions with large gradients leads to significant errors. We consider two approaches for increase of accuracy of interpolation: a fitting of the interpolation formula to a boundary layer component and the application of polynomial interpolation on Shishkin mesh. Numerical results are discussed.

Keywords

  • Function of two variables
  • Boundary layer
  • Polynomial interpolation
  • Shishkin mesh
  • Nonpolynomial interpolation

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References

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Acknowledgements

Supported in part by Russian Foundation for Basic Research under Grants 15-01-06584, 16-01-00727.

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Correspondence to Alexander Zadorin .

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Zadorin, A. (2017). Two-Dimensional Interpolation of Functions with Large Gradients in Boundary Layers. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_88

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_88

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57098-3

  • Online ISBN: 978-3-319-57099-0

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