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Discretisations of Reaction-Convection-Diffusion Problems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1985)

Abstract

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

$$ - E^2 u'' + Au = f\;\;{\rm in}\;{\rm (0,1),}\;\;\;\;u(0) = \gamma _0 ,\;\;u(1) = \gamma _1 .$$

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Correspondence to Torsten Linß .

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Linß, T. (2010). Discretisations of Reaction-Convection-Diffusion Problems. In: Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems. Lecture Notes in Mathematics(), vol 1985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05134-0_6

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