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A Tailored Finite Point Method for Convection-Diffusion-Reaction Problems

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An Erratum to this article was published on 16 April 2010

An Erratum to this article was published on 16 April 2010

Abstract

We study a tailored finite point method (TFPM) for solving the convection-diffusion-reaction equation. The solution basis functions for the TFPM are constructed for a 5 point, 7 point and 9 point stencil. Some truncation error calculations are given. Numerical tests are given on problems containing a boundary or interior layer. The tests compare TFPM with several versions of a Petrov-Galerkin finite element schemes, and suggest that TFPM gives a superior resolution of the layers.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Chung Hsing University, 250 Kuo-Kuang Road, Taichung, 40227, Taiwan

    Yintzer Shih & Peishan Tsai

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    R. Bruce Kellogg

Authors
  1. Yintzer Shih
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  2. R. Bruce Kellogg
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  3. Peishan Tsai
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Correspondence to Yintzer Shih.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s10915-010-9362-5

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Shih, Y., Kellogg, R.B. & Tsai, P. A Tailored Finite Point Method for Convection-Diffusion-Reaction Problems. J Sci Comput 43, 239–260 (2010). https://doi.org/10.1007/s10915-010-9354-5

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  • DOI: https://doi.org/10.1007/s10915-010-9354-5

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