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International Conference on Numerical Analysis and Its Applications

NAA 2000: Numerical Analysis and Its Applications pp 18–26Cite as

A Parameter Robust Method for a Problem with a Symmetry Boundary Layer

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

Abstract

We consider the classical problem of a two-dimensional laminar jet of incompressible fluid flowing into a stationary medium of the same fluid [2]. The equations of motion are the same as the boundary layer equations for flow over an infinite flat plate, but with different boundary conditions. Numerical experiments show that, using an appropriate piecewise uniform mesh, numerical solutions are obtained which are parameter robust with respect to both the number of mesh nodes and the number of iterations required for convergence.

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References

  1. Prandtl, L., Tietjens, O. G., Applied Hydro-and Aeromechanics, Dover Publications,New York (1957)

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  2. Schlichting, H., Boundary-layer theory, 7th ed. McGraw Hill, New York (1979)

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  3. Acheson, D. J., Elementary Fluid Dynamics, Oxford University Press, Oxford (1990)

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  4. Warsi, Z. U. A., Fluid dynamics: theoretical and computational approaches, CRC Press, Boca Raton (1993)

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  5. Hegarty, A. F., Miller J. J. H., OŔiordan E., Shishkin, G. I., Special meshes for finite difference approximations to an advection-diffusion equation with parabolic layers, Journal of Computational Physics, Vol. 117, (1995) 47–54

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  6. Miller, J. J. H., OŔiordan, E., Shishkin, G. I., Fitted numerical methods for singular perturbation problems, World Scientific, London (1996)

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  7. Farrell, P. A., Hegarty, A. F., Miller, J. J. H., OŔiordan, E., Shishkin, G. I., Robust Computational Techniques for Boundary Layers, Chapman & Hall/CRC Press, Boca Raton (2000)

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Author information

Authors and Affiliations

  1. Department of Mathematics & Statistics, University of Limerick, Limerick, Ireland

    Ali R. Ansari & Alan F. Hegarty

  2. Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ekaterinburg, Russia

    Grigorii I. Shishkin

Authors
  1. Ali R. Ansari
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  2. Alan F. Hegarty
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  3. Grigorii I. Shishkin
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rousse, 7000, Rousse, Bulgaria

    Lubin Vulkov  & Plamen Yalamov  & 

  2. UNI-C,Danish Computing Center for Research and Education, DTU,Building 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2001 Springer-Verlag Berlin Heidelberg

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Ansari, A.R., Hegarty, A.F., Shishkin, G.I. (2001). A Parameter Robust Method for a Problem with a Symmetry Boundary Layer. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_3

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  • DOI: https://doi.org/10.1007/3-540-45262-1_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

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