2010 | OriginalPaper | Chapter
Introduction
Author : Torsten Linß
Published in: Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Stationary linear reaction-convection-diffusion problems form the subject of this monograph:
$$ - \in u^ - bu^{'} + cu = f\text{ in (0,1), }u(0) = \gamma _0 ,\text{ }u(1) = \gamma _1 $$
and its two-dimensional analogue
$$ - \in \Delta u - b \cdot \nabla u + cu = f\text{ in }\Omega \subset \text{ }IR^2 \text{, }u|\partial \Omega = g$$
with a small positive parameter ε.
Such problems arise in various models of fluid flow [52,53,73]; they appear in the (linearised) Navier-Stokes and in the Oseen equations, in the equations modelling oil extraction from underground reservoirs [32], flows in chemical reactors [3] and convective heat transport with large Péclet number [56]. Other applications include the simulation of semiconductor devices [130].