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Parameter-uniform numerical method for singularly perturbed convection-diffusion problem on a circular domain

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Abstract

A linear singularly perturbed elliptic problem, of convection-diffusion type, posed on a circular domain is examined. Regularity constraints are imposed on the data in the vicinity of the two characteristic points. The solution is decomposed into a regular and a singular component. A priori parameter-explicit pointwise bounds on the partial derivatives of these components are established. By transforming to polar co-ordinates, a monotone finite difference method is constructed on a piecewise-uniform layer-adapted mesh of Shishkin type. Numerical analysis is presented for this monotone numerical method. The numerical method is shown to be parameter-uniform. Numerical results are presented to illustrate the theoretical error bounds established.

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Authors and Affiliations

  1. MACSI, Department of Mathematics and Statistics, University of Limerick, Plassey, Limerick, Ireland

    A. F. Hegarty

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

    E. O’Riordan

Authors
  1. A. F. Hegarty
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  2. E. O’Riordan
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Correspondence to E. O’Riordan.

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Communicated by: Zydrunas Gimbutas

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Hegarty, A.F., O’Riordan, E. Parameter-uniform numerical method for singularly perturbed convection-diffusion problem on a circular domain. Adv Comput Math 43, 885–909 (2017). https://doi.org/10.1007/s10444-016-9510-z

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  • DOI: https://doi.org/10.1007/s10444-016-9510-z

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