Characteristic Tailored Finite Point Method for Convection-Dominated Convection-Diffusion-Reaction Problems

• Published in: Journal of scientific computing Vol. 47; no. 2; pp. 198 - 215
• Main Authors: Shih, Yintzer, Kellogg, R. Bruce, Chang, Yoyo
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.05.2011; Springer Nature B.V
• Subjects: Algorithms; Boundary layer; Boundary layers; Computation; Computational Mathematics and Numerical Analysis; Construction; Convection-diffusion equation; Diffusion coefficient; Diffusion layers; Finite element method; Mathematical analysis; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical models; Mathematics; Mathematics and Statistics; Reaction-diffusion equations; Theoretical; Tailored finite point; Internal layer; Convection-diffusion-reaction; Characteristic; Finite element; Boundary layer
• ISSN: 0885-7474; 1573-7691
• DOI: 10.1007/s10915-010-9433-7

In this paper, we propose a characteristic tailored finite point method (CTFPM) for solving the convection-diffusion-reaction equation with variable coefficients. We develop an algorithm to construct a streamline-aligned grid for the CTFPM. Our numerical tests show for small diffusion coefficient the CTFPM solution resolves the internal and boundary layers regardless the mesh size, and depicts that CTFPM method with a streamline grid has excellent performance compared with the tailored finite point method and a streamline upwind finite element method when ε is small.