Green's function estimates for a 2d singularly perturbed convection-diffusion problem: extended analysis
Abstract
This paper presents an extended version of the article [Franz, S., Kopteva, N.: J. Differential Equations, 252 (2012)]. The main improvement compared to the latter is in that here we additionally estimate the mixed second-order derivative of the Green's function. The case of Neumann conditions along the characteristic boundaries is also addressed. A singularly perturbed convection-diffusion problem is 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 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.
Cite
@article{arxiv.2212.11916,
title = {Green's function estimates for a 2d singularly perturbed convection-diffusion problem: extended analysis},
author = {Sebastian Franz and Natalia Kopteva},
journal= {arXiv preprint arXiv:2212.11916},
year = {2022}
}
Comments
Extended version of [Franz, S., Kopteva, N.: J. Differential Equations, 252 (2012)]. arXiv admin note: substantial text overlap with arXiv:1103.2948