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Convection-Diffusion Problems

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

Abstract

This chapter is devoted to numerical methods for the convection-diffusion problem

$$- \varepsilon \Delta u - b\nabla u + cu = f\;in\;\Omega = (0,1)^2 ,\;u|_{\partial \Omega } = 0,$$
(9.1)

with b 1 ≥ β1 > 0, b 2 ≥ β2 > 0 on [0,1]2, i.e., problems with regular boundary layers at the outflow boundary x = 0 and y = 0. The analytical behaviour of the solution of (9.1) was studied in Sect. 7.3.1.

Results for problems with characteristic layers will only be mentioned briefly.

Keywords

  • Interpolation Error
  • Richardson Extrapolation
  • Inverse Inequality
  • Shishkin Mesh
  • Bilinear Element

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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© 2010 Springer-Verlag Berlin Heidelberg

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Linß, T. (2010). 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_9

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