Abstract
This chapter deals with finite elements defined on a simplex (triangle in 2D, tetrahedron in 3D). The degrees of freedom are either nodal values at some points on the simplex or integrals over the faces or the edges of the simplex, and the associated functional space is composed of multivariate polynomials of prescribed total degree. We focus our attention on scalar-valued finite elements. The results extend to the vector-valued case by reasoning componentwise.
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). Simplicial finite elements. In: Finite Elements I. Texts in Applied Mathematics, vol 72. Springer, Cham. https://doi.org/10.1007/978-3-030-56341-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-56341-7_7
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)