Crouzeix-Raviart triangular elements are inf-sup stable
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} $p$.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2021
- DOI:
- 10.48550/arXiv.2105.14987
- arXiv:
- arXiv:2105.14987
- Bibcode:
- 2021arXiv210514987C
- Keywords:
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- Mathematics - Numerical Analysis
- E-Print:
- 18 pages, 1 figure