Greenʼs function estimates for a singularly perturbed convection–diffusion problem

Sebastian Franz, Natalia Kopteva

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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.
Original languageEnglish
Pages (from-to)1521-1545
Number of pages25
JournalJournal of Differential Equations
Issue number2
Publication statusPublished - 15 Jan 2012


  • Green's function
  • singular perturbations
  • convection-diffusion


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