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

Date
2012
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 L-1 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. (C) 2011 Elsevier Inc. All rights reserved.
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peer-reviewed
Publisher
Elsevier
Citation
Journal of Differential Equations;252 (2), pp. 1521-1545
Collections
Mathematics & Statistics
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FrKopt_10_rev_11.pdf
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Keywords
Green's function, singular perturbations, convection-diffusion, corner singularities, elliptic problems, boundary-layers
ULRR Identifiers
https://hdl.handle.net/10344/5773
 https://doi.org/10.34961/4158
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Funding Information
Science Foundation Ireland (SFI)
Sustainable Development Goals
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