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Finite Difference Schemes for 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 finite-difference discretisations of the stationary linear convection-diffusion problem

$$Lu\,: = - \varepsilon u'' - bu' + cu = f\,\,{\rm in}\,(0,1),\;\;u(0) = \gamma _0 ,\;u(1) = \gamma _1 ,$$

with b ≥ β > 0 on [0, 1]. For the sake of simplicity we shall assume that

$$c \ge 0\,\,{\rm and}\;\;{\rm b'} \ge 0\;\;\;\;\;{\rm on[0,1]}{\rm .}$$

Using (4.1) as a model problem, a general convergence theory for certain firstand second-order upwinded difference schemes on arbitrary and on layer-adapted meshes is derived. The close relationship between the differential operator and its upwinded discretisations is highlighted.

Keywords

  • Difference Scheme
  • Truncation Error
  • Finite Difference Scheme
  • Upwind Scheme
  • Richardson Extrapolation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Torsten Linß .

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Linß, T. (2010). Finite Difference Schemes for 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_4

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