Singularly perturbed convection-diffusion problems with boundary and weak interior layers

Authors:
P. A. Farrell;A. F. Hegarty;J. J. H. Miller;E. O'Riordan;G. I. Shishkin
Affiliations:
Department of Computer Science, Kent State University, Kent, OH;Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland;Department of Mathematics, Trinity College, Dublin, Ireland;Institute for Mathematics and Mechanics, Russian Academy of Sciences, Ural Branch, Ekaterinburg, Russia;School of Mathematical Sciences, Dublin City University, Dublin, Ireland
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
Year:
2004

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Abstract

In this paper a singularly perturbed convection-diffusion equation with a discontinuous source term is examined. Boundary and weak interior layers appear in the solution. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter.