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Multiscale Convection in One Dimensional Singularly Perturbed Convection–Diffusion Problems

  • E. O’Riordan
  • J. Quinn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)

Abstract

Linear singularly perturbed ordinary differential equations of convection diffusion type are considered. The convective coefficient varies in scale across the domain which results in interior layers appearing in areas where the convective coefficient decreases from a scale of order one to the scale of the diffusion coefficient. Appropriate parameter-uniform numerical methods are constructed. Numerical results are given to illustrate the theoretical error bounds established.

Keywords

Uniform Mesh Convective Coefficient Regular Component Interior Layer Singular Perturbation Parameter 
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References

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    de Falco, C., O’ Riordan, E.: A parameter robust Petrov-Galerkin scheme for advection-diffusion-reaction equations. Numerical Algorithms 5(1), 107–127 (2011)CrossRefGoogle Scholar
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    Farrell, P.A., Hegarty, A.F., Miller, J.J.H., O’Riordan, E., Shishkin, G.I.: Robust computational techniques for boundary layers. Chapman and Hall/CRC Press, Boca Raton, U.S.A (2000)zbMATHGoogle Scholar
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    Farrell, P.A., Hegarty, A.F., Miller, J.J.H., O’ Riordan, E., Shishkin, G.I.: Singularly perturbed convection diffusion problems with boundary and weak interior layers. Journal Computational and Applied Mathematics 166(1), 133–151 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
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    O’ Riordan, E., Quinn, J.: Parameter-uniform numerical methods for some Linear and Nonlinear Singularly Perturbed Convection Diffusion Boundary Turning Point Problems. BIT Numerical Mathematics 51, 317–337 (2011)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • E. O’Riordan
    • 1
  • J. Quinn
    • 1
  1. 1.School of Mathematical SciencesDublin City UniversityDublinIreland

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