Crouzeix-Raviart triangular elements are inf-sup stable

The Crouzeix-Raviart triangular finite elements are inf \inf - form="prefix">sup encoding="application/x-tex">\sup stable for the Stokes equations any mesh with at least one interior vertex. This result affirms a conjecture of Crouzeix-Falk from 1989 alttext="p equals 3"> p = 3 encoding="application/x-tex">p=3 . Our proof applies to any odd degree greater-than-or-equal-to ? encoding="application/x-tex">p\ge 3 and concludes overall stability analysis: degree alttext="p"> encoding="application/x-tex">p in two dimensions piecewise polynomials minus 1"> ?<!-- ? <mml:mn>1 encoding="application/x-tex">p-1 vanishing integral form pair for all positive integers