A Tailored Finite Point Method for Convection-Diffusion-Reaction Problems Yintzer Shih †‡ R. Bruce Kellogg § Peishan Tsai ‡ 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. Keywords: Tailored finite point, convection-diffusion-reaction, finite element, boundary layer, internal layer Running Title. A Tailored Finite Point Method for Convection-Diffusion- Reaction Problems Address for manuscript correspondence. Assistant Prof. Yin-Tzer Shih, Department of Applied Mathematics, National Chung Hsing University; 250 Kuo-Kuang Road, Taichung 40227, Taiwan; e-mail: yintzer shih@email.nchu.edu.tw; phone: +886-4-2285-3459; fax: +816-4-2287-3028. † Corresponding author: yintzer shih@email.nchu.edu.tw ‡ Department of Applied Mathematics, National Chung Hsing University, Taichung 40227, Taiwan. § Department of Mathematics, University of South Carolina, SC 29208, USA 1