This chapter is devoted to developing function spaces that are used in the variational formulation of differential equations. We begin with a review of Lebesgue integration theory, upon which our notion of “variational” or “weak” derivative rests. Functions with such “generalized” derivatives make up the spaces commonly referred to as Sobolev spaces. We develop only a small fraction of the known theory for these spaces—just enough to establish a foundation for the finite element method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
(2008). Sobolev Spaces. In: The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-0-387-75934-0_2
Download citation
DOI: https://doi.org/10.1007/978-0-387-75934-0_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-75933-3
Online ISBN: 978-0-387-75934-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)