A Finite-Element Singular-Perturbation Technique for Convection-Diffusion Problems—Part 1: The One-Dimensional Case

[+] Author and Article Information
Rafael F. Diaz-Munio, L. Carter Wellford

Department of Civil Engineering, University of Southern California, University Park, Los Angeles, Calif. 90007

J. Appl. Mech 48(2), 265-271 (Jun 01, 1981) (7 pages) doi:10.1115/1.3157608 History: Received December 01, 1979; Revised September 01, 1980; Online July 21, 2009


Approximation procedures for the solution of convection-diffusion equations, occurring in various physical problems, are considered. Several finite-element algorithms based on singular-perturbation methods are proposed for the solution of these equations. A method of variational matched asymptotic expansions is employed to develop shape functions which are particularly useful when convection effects dominate diffusion effects in these problems. When these shape functions are used, in conjunction with the standard Galerkin method, to solve convection-diffusion equations, increased solution accuracy is obtained. Numerical results for various one-dimensional problems are presented to establish the workability of the developed methods.

Copyright © 1981 by ASME
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