Singularly perturbed parabolic problems with non-smooth data

Authors:
E. O'Riordan;G. I. Shishkin
Affiliations:
School of Mathematical Sciences, Dublin City University, Dublin, Ireland;Institute for Mathematics and Mechanics, Russian Academy of Sciences, Ekaterinburg, Russia
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 class of singularly perturbed parabolic equations with discontinuous data is examined. Interior layers appear in the solutions of problems in this class. A numerical method is constructed for this class of problems which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter.