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

Authors:
Yintzer Shih;R. Bruce Kellogg;Peishan Tsai
Affiliations:
Department of Applied Mathematics, National Chung Hsing University, Taichung, Taiwan 40227;Department of Mathematics, University of South Carolina, Columbia, USA 29208;Department of Applied Mathematics, National Chung Hsing University, Taichung, Taiwan 40227
Venue:
Journal of Scientific Computing
Year:
2010

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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.