Abstract
In this chapter and the next one, we study the interpolation operators associated with the finite elements introduced in Chapters 14 and 15. We consider a shape-regular sequence of affine simplicial meshes with a generation-compatible orientation. In the present chapter, we show how the degrees of freedom attached to the faces and the edges can be extended to Sobolev spaces with enough smoothness. On the way, we discover fundamental commuting properties of the interpolation operators embodied in the de Rham complex.
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ern, A., Guermond, JL. (2021). Local interpolation in \({{{\varvec{H}}(\text {div})}}\) and \({{{\varvec{H}}(\text {curl})}}\) (I). In: Finite Elements I. Texts in Applied Mathematics, vol 72. Springer, Cham. https://doi.org/10.1007/978-3-030-56341-7_16
Download citation
DOI: https://doi.org/10.1007/978-3-030-56341-7_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-56340-0
Online ISBN: 978-3-030-56341-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)