Abstract
In this chapter we study the important transport equation that models transport of various physical quantities, such as density, momentum, and energy, for instance. In particular, the transportation of heat through convection is modeled by this equation. That is, the transfer of heat by some external physical process, such as air blown by a fan, or a moving fluid, for instance. Often, high convection takes place alongside low diffusion (i.e., uniform spreading) of heat, leading to large temperature gradients. As we shall see, this may cause numerical instabilities unless special care is taken. To do so, we introduce the Galerkin Least Squares (GLS) method, which is more robust than the standard Galerkin method. We illustrate with numerical examples.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C. Johnson. Numerical Solution of Partial Differential Equations by the Finite Element Method. Studentlitteratur, 1987.
H. G. Roos, M. Stynes, and L. Tobiska. Numerical Methods for Singularly Perturbed Differential Equations. Springer, 1996.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Larson, M.G., Bengzon, F. (2013). Transport Problems. In: The Finite Element Method: Theory, Implementation, and Applications. Texts in Computational Science and Engineering, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33287-6_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-33287-6_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33286-9
Online ISBN: 978-3-642-33287-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)