Full analysis of the Green's function for a singularly perturbed convection-diffusion problem in three dimensions
Abstract
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 L1 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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