Abstract
One of the virtues of the variational approach is that it leads naturally to a whole family of approximation methods. Let us emphasize again that the reason why approximation methods for PDEs are needed is that, even though we may be able to prove the existence of a solution, in general there is no closed form formula for it. There are other approximation methods that are not variational, such as the finite difference method seen earlier, the finite volume method that we will see in Chap. 10, and yet many other methods that we will not consider in this book.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
This is an elliptic regularity estimate.
- 2.
This right-hand side is an approximation of the Dirac mass \(\delta _{\frac{1}{2}}\).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Le Dret, H., Lucquin, B. (2016). Variational Approximation Methods for Elliptic PDEs. In: Partial Differential Equations: Modeling, Analysis and Numerical Approximation. International Series of Numerical Mathematics, vol 168. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-27067-8_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-27067-8_5
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-27065-4
Online ISBN: 978-3-319-27067-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)