In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference operator to construct a parameter-uniform numerical method for this class of singularly perturbed problems.
@article{bwmeta1.element.doi-10_2478_s11533-011-0121-0,
author = {Eugene O'Riordan},
title = {Opposing flows in a one dimensional convection-diffusion problem},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {85-100},
zbl = {1259.65122},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0121-0}
}
Eugene O’Riordan. Opposing flows in a one dimensional convection-diffusion problem. Open Mathematics, Tome 10 (2012) pp. 85-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0121-0/
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