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 language | English |
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Pages (from-to) | 1521-1545 |
Number of pages | 25 |
Journal | Journal of Differential Equations |
Volume | 252 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Jan 2012 |
Keywords
- 35J08
- 35J25
- 65N15
- Convection-diffusion
- Green's function
- Singular perturbations