Abstract
This chapter is concerned with finite-difference discretisations of the stationary linear convection-diffusion problem
with b ≥ β > 0 on [0, 1]. For the sake of simplicity we shall assume that
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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© 2010 Springer-Verlag Berlin Heidelberg
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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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DOI: https://doi.org/10.1007/978-3-642-05134-0_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05133-3
Online ISBN: 978-3-642-05134-0
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