On the Inf-Sup Stability of Crouzeix-Raviart Stokes Elements in 3D
Numerical Analysis
2022-11-16 v2 Numerical Analysis
Abstract
We consider non-conforming discretizations of the stationary Stokes equation in three spatial dimensions by Crouzeix-Raviart type elements. The original definition in the seminal paper by M. Crouzeix and P.-A. Raviart in 1973 is implicit and also contains substantial freedom for a concrete choice. In this paper, we introduce basic Crouzeix-Raviart basis functions in 3D in analogy to the 2D case in a fully explicit way. We prove that this basic CrouzeixRaviart element for the Stokes equation is inf-sup stable for polynomial degree (quadratic velocity approximation). We identify spurious pressure modes for the conforming 3D Stokes element and show that these are eliminated by using the basic Crouzeix-Raviart space.
Keywords
Cite
@article{arxiv.2205.00062,
title = {On the Inf-Sup Stability of Crouzeix-Raviart Stokes Elements in 3D},
author = {Stefan Sauter and Céline Torres},
journal= {arXiv preprint arXiv:2205.00062},
year = {2022}
}