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 (https://doi.org/10.1016/j.jde.2011.07.033)

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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.

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• Item metadata

  Item type:	Article
  ID code:	44835
  Dates:	Date Event 15 January 2012 Published
  Subjects:	Science > Mathematics > Probabilities. Mathematical statistics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Pure Administrator
  Date deposited:	13 Sep 2013 10:43
  Last modified:	08 Apr 2024 20:43
  URI:	https://strathprints.strath.ac.uk/id/eprint/44835