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Greenʼs function estimates for a singularly perturbed convection–diffusion problem

Franz, Sebastian and Kopteva, Natalia (2012) Greenʼs function estimates for a singularly perturbed convection–diffusion problem. Journal of Differential Equations, 252 (2). pp. 1521-1545. ISSN 0022-0396

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    Abstract

    We consider a singularly perturbed convection-diusion problem posed in the unit square with a horizontal convective direction. Its solutions exhibit parabolic and exponential boundary layers. Sharp estimates of the Green's function and its first- and second-order derivatives are derived in the L1 norm. The dependence of these estimates on the small diusion parameter is shown explicitly. The obtained estimates will be used in a forthcoming numerical analysis of the considered problem.