An Accurate Numerical Solution of a Two Dimensional Heat Transfer Problem with a Parabolic Boundary Layer
Year: 1998
Author: C. Clavero, J.J.H. Miller, E. O'Riordan, G.I. Shishkin
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 1 : pp. 27–39
Abstract
A singularly perturbed linear convection-diffusion problem for heat transfer in two dimensions with a parabolic boundary layer is solved numerically. The numerical method consists of a special piecewise uniform mesh condensing in a neighbourhood of the parabolic layer and a standard finite difference operator satisfying a discrete maximum principle. The numerical computations demonstrate numerically that the method is $ε$-uniform in the sense that the rate of convergence and error constant of the method are independent of the singular perturbation parameter $ε$. This means that no matter how small the singular perturbation parameter $ε$ is, the numerical method produces solutions with guaranteed accuracy depending solely on the number of mesh points used.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1998-JCM-9139
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 1 : pp. 27–39
Published online: 1998-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Linear convection-diffusion parabolic layer piecewise uniform mesh finite difference.