Year: 2021
Type: preprint
Abstract: The Crouzeix-Raviart triangular finite elements are $\inf$-$\sup$ stable for the Stokes equations for any mesh with at least one interior vertex. This result affirms a {\em conjecture of Crouzeix-Falk} from 1989 for $p=3$. Our proof applies to {\em any odd degree} $p\ge 3$ and hence Crouzeix-Raviart triangular finite elements of degree $p$ in two dimensions and the piecewise polynomials of degree $p-1$ with vanishing integral form a stable Stokes pair {\em for all positive integers} $p$.
Source: arXiv (Cornell University)
Authors: Carstensen, C., Sauter, S.
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4290095575