Abstract
In this chapter we consider finite element and finite volume discretisations of
with b ≥ β > 0. Its associated variational formulation is: Find \(u \in H_0^1 (0,1)\) such that
where
and
Throughout assume that
This condition guaranties the coercivity of the bilinear form in (5.2):
This is verified using standard arguments, see e.g. [141]. If b ≥ β > 0 then (5.4) can always be ensured by a transformation \(\bar u(x) = u(x)e^{\delta x}\) with δ chosen appropriately. We assume this transformation has been carried out.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Keywords
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Linß, T. (2010). Finite Element and Finite Volume Methods. 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_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-05134-0_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05133-3
Online ISBN: 978-3-642-05134-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)