Full analysis of the Green's function for a singularly perturbed convection-diffusion problem in three dimensions

Details Full analysis of the Green's function for a singularly perturbed convection-diffusion problem in three dimensions Full analysis of the Green's function for a singularly perturbed convection-diffusion problem in three dimensions

2011-03-15

arxiv.org/abs/1103.2948v2

Mathematics

Numerical Analysis

25 pages, 2 figures

Scientific paper

A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its derivatives are established in the $L_1$ norm. The dependence of these bounds on the small perturbation parameter is shown explicitly. The obtained estimates will be used in a forthcoming numerical analysis of the considered problem. The present article is a more detailed version of our recent paper [7].

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