Crouzeix-Raviart triangular elements are inf-sup stable

05/31/2021

∙

by   C. Carstensen, et al.

∙

0

∙

share

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 conjecture of Crouzeix-Falk from 1989 for p=3. Our proof applies to any odd degree p≥ 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 for all positive integers p.