This paper shows the usefulness of the exponential upwinding technique in convection diffusion computations. In particular, it is demonstrated that, even when convection is dominant, if exponential upwinding is employed in conjunction with either the Jacobi or the Gauss-Seidel iteration process, one can obtain computed solutions that are accurate and free of unphysical oscillations
Cite this paper
H. Godinez and V. Manoranjan, "Modeling Convection Diffusion with Exponential Upwinding," Applied Mathematics
, Vol. 4 No. 8, 2013, pp. 80-88. doi: 10.4236/am.2013.48A011
 D. F. Griffiths and A. R. Mitchell, “On Generating Up wind Finite Element Methods,” Finite Element Methods for Convection Dominated Flows, Vol. 34, 1979, pp. 91-104.
 G. H. Golub and C. F. Van Loan, “Matrix Computations,” The Johns Hopkins University Press, Baltimore, 1990.
 R. S. Varga, “Matrix Iterative Analysis,” Prentice-Hall, Upper Saddle River, 1962.
 V. S. Manoranjan and R. Drake, “A Spectrum Enveloping Technique for Convection-Diffusion Computations,” IMA Journal of Numerical Analysis, Vol. 13, No. 3, 1993, pp. 431-443. doi:10.1093/imanum/13.3.431
 R. Wait and A. R. Mitchell, “Finite Element Analysis and Applications,” John Wiley and Sons, New York, 1985.
 A. R. Mitchell, “Computational Methods in Partial Dif ferential Equations,” John Wiley and Sons, London, 1969.
 K. W. Morton and D. F. Mayers, “Numerical Solution of Partial Differential Equations,” Cambridge University Press, Cambridge, 2001.
 V. S. Manoranjan and M. O. Gomez, “Alternating Direc tion Implicit Method with Exponential Upwinding,” Com puters & Mathematics with Applications, Vol. 30, No. 11, 1995, pp. 47-58. doi:10.1016/0898-1221(95)00163-S