Abstract
We consider a singularly perturbed convection–diffusion problem posed in the unit square with a horizontal convective direction. Its solutions exhibit parabolic and exponential boundary layers. Sharp estimates of the Greenʼs function and its first- and second-order derivatives are derived in the L 1 norm. The dependence of these estimates on the small diffusion parameter is shown explicitly. The obtained estimates will be used in a forthcoming numerical analysis of the considered problem.
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