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

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Numerical Analysis and Its Applications (NAA 2016)

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

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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.

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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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Authors and Affiliations

  1. Sobolev Mathematics Institute SB RAS, Omsk Branch, Pevtsova 13, Omsk, 644043, Russia

    Alexander Zadorin

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  1. Alexander Zadorin
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Correspondence to Alexander Zadorin .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. Department of Applied Mathematics and Statistics, University of Rousse, Ruse, Bulgaria

    Lubin Vulkov

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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

  • eBook Packages: Computer ScienceComputer Science (R0)

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