A family of higher-order numerical schemes for the convection-diffusion equation in conservation form

Article type: Research Article

Authors: McCartin, Brian J.^{; *} | Fisackerly, Michael W.

Affiliations: Applied Mathematics, Kettering University, Flint, MI 48504-4898, USA

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this paper, we introduce a class of compact, higher-order, exponentially-fitted discretizations of the steady, one-dimensional convection-diffusion equation in conservation form. This will be achieved by employing the Mehrstellenverfahren technique of L. Collatz. These new schemes are shown to be uniformly second order accurate in the small parameter ε (the diffusion). The fourth-order accurate member of this family of schemes is studied in detail. Theoretical and numerical comparisons will be made to the methods of Allen-Southwell, El-Mistikawy-Werle, Leventhal, and Gartland. Additional examples exercising this new scheme are presented.

Keywords: Exponential fitting, Mehrstellenverfahren, convection-diffusion equation

DOI: 10.3233/JCM-2005-5108

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 5, no. 1, pp. 91-108, 2005