Full analysis of the Green's function for a singularly perturbed convection-diffusion problem in three dimensions
Provides theoretical estimates needed for numerical analysis of a specific class of PDEs, but is incremental as it extends prior work to 3D with more detail.
Sharp bounds for the Green's function and its derivatives in the L1 norm are established for a 3D singularly perturbed convection-diffusion problem with characteristic layers, with explicit dependence on the perturbation parameter.
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].