Green's function estimates for a singularly perturbed convection-diffusion problem

Sebastian Franz, Natalia Kopteva

Research output: Contribution to journalArticlepeer-review

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 Green's function and its first- and second-order derivatives are derived in the L1 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.

Original languageEnglish
Pages (from-to)1521-1545
Number of pages25
JournalJournal of Differential Equations
Volume252
Issue number2
DOIs
Publication statusPublished - 15 Jan 2012

Keywords

  • 35J08
  • 35J25
  • 65N15
  • Convection-diffusion
  • Green's function
  • Singular perturbations

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