2021/05/31 by C. Carstensen, Carstensen, C., S. Sauter +1
Earth and Planetary Sciences · Engineering · Mathematics · #Enhanced Oil Recovery Techniques #FOS: Mathematics #Geological formations and processes #Navier-Stokes equation solutions #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2105.14987
openalex publication_date 2021/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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≥ 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.