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.
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 language | English |
|---|---|
| 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
- Green's function
- singular perturbations
- convection-diffusion