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A parameter-uniform numerical method for a singularly perturbed two parameter elliptic problem

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Abstract

In this paper, a class of singularly perturbed elliptic partial differential equations posed on a rectangular domain is studied. The differential equation contains two singular perturbation parameters. The solutions of these singularly perturbed problems are decomposed into a sum of regular, boundary layer and corner layer components. Parameter-explicit bounds on the derivatives of each of these components are derived. A numerical algorithm based on an upwind finite difference operator and a tensor product of piecewise-uniform Shishkin meshes is analysed. Parameter-uniform asymptotic error bounds for the numerical approximations are established.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland

    E. O’Riordan

  2. Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland

    M. L. Pickett

Authors
  1. E. O’Riordan
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  2. M. L. Pickett
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Correspondence to E. O’Riordan.

Additional information

Communicated by Martin Stynes.

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O’Riordan, E., Pickett, M.L. A parameter-uniform numerical method for a singularly perturbed two parameter elliptic problem. Adv Comput Math 35, 57–82 (2011). https://doi.org/10.1007/s10444-010-9164-1

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  • DOI: https://doi.org/10.1007/s10444-010-9164-1

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