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Published in:
2010 | OriginalPaper | Chapter
Discretisations of Reaction-Convection-Diffusion Problems
Author : Torsten Linß
Published in: Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems
Publisher: Springer Berlin Heidelberg
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This chapter is concerned with discretisations of the stationary linear reaction- 4 convection-diffusion problem
$$ - \varepsilon _d u^ - \varepsilon _c bu + cu = f\text{ in (0,1), }u(0) = \gamma _0 ,u(1) = \gamma _1 ,$$
with
b
≥ 1 and
c
≥ 1 on [0, 1].
In particular, we shall study the special case of scalar reaction-diffusion problems
$$ - \varepsilon _d u^ - \varepsilon _c bu + cu = f\text{ in (0,1), }u(0) = \gamma _0 ,u(1) = \gamma _1 ,$$
and its vector-valued counterpart
$$ - E^2 u'' + Au = f\;\;{\rm in}\;{\rm (0,1),}\;\;\;\;u(0) = \gamma _0 ,\;\;u(1) = \gamma _1 .$$