Header

UZH-Logo

Maintenance Infos

A family of Crouzeix–Raviart finite elements in 3D


Ciarlet, Patrick; Dunkl, Charles F; Sauter, Stefan A (2018). A family of Crouzeix–Raviart finite elements in 3D. Analysis and Applications, 16(05):649-691.

Abstract

In this paper, we will develop a family of non-conforming “Crouzeix–Raviart” type finite elements in three dimensions. They consist of local polynomials of maximal degree $\rho \in \mathbb{N}$ on simplicial finite element meshes while certain jump conditions are imposed across adjacent simplices. We will prove optimal a priori estimates for these finite elements. The characterization of this space via jump conditions is implicit and the derivation of a local basis requires some deeper theoretical tools from orthogonal polynomials on triangles and their representation. We will derive these tools for this purpose. These results allow us to give explicit representations of the local basis functions. Finally, we will analyze the linear independence of these sets of functions and discuss the question whether they span the whole non-conforming space.

Abstract

In this paper, we will develop a family of non-conforming “Crouzeix–Raviart” type finite elements in three dimensions. They consist of local polynomials of maximal degree $\rho \in \mathbb{N}$ on simplicial finite element meshes while certain jump conditions are imposed across adjacent simplices. We will prove optimal a priori estimates for these finite elements. The characterization of this space via jump conditions is implicit and the derivation of a local basis requires some deeper theoretical tools from orthogonal polynomials on triangles and their representation. We will derive these tools for this purpose. These results allow us to give explicit representations of the local basis functions. Finally, we will analyze the linear independence of these sets of functions and discuss the question whether they span the whole non-conforming space.

Statistics

Citations

Dimensions.ai Metrics
2 citations in Web of Science®
2 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

22 downloads since deposited on 01 Nov 2018
8 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Analysis
Physical Sciences > Applied Mathematics
Language:English
Date:2018
Deposited On:01 Nov 2018 11:47
Last Modified:29 Jul 2020 07:13
Publisher:World Scientific Publishing Co. Pte. Ltd.
ISSN:0219-5305
Additional Information:Electronic version of an article published as Analysis and Applications, [16, No. 05, 2018, 649-691] DOI: 10.1142/S0219530518500070] © copyright World Scientific Publishing Company https://www.worldscientific.com/worldscinet/aa
OA Status:Green
Publisher DOI:https://doi.org/10.1142/S0219530518500070

Download

Green Open Access

Download PDF  'A family of Crouzeix–Raviart finite elements in 3D'.
Preview
Content: Accepted Version
Language: English
Filetype: PDF
Size: 1MB
View at publisher