Volume 2, Issue 2
Green's Function Estimates for a Singularly Perturbed Convection-Diffusion Problem in Three Dimensi

Sebastian Franz and Natalia Kopteva

Int. J. Numer. Anal. Mod. B, 2 (2011), pp. 124-141

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  • 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 firstand second-order derivatives are established in the L_1 norm by employing the parametrix metho'. 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 to derive a robust a posteriori error estimator in the maximum norm.

  • History

Published online: 2011-02

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