On the inf-sup stability of Crouzeix-Raviart Stokes elements in 3D.
- Resource Type
- Article
- Authors
- Sauter, Stefan; Torres, Céline
- Source
- Mathematics of Computation. May2023, Vol. 92 Issue 341, p1033-1059. 27p.
- Subject
- *STOKES equations
*VELOCITY
*ANALOGY
*POLYNOMIALS
- Language
- ISSN
- 0025-5718
We consider discretizations of the stationary Stokes equation in three spatial dimensions by non-conforming Crouzeix-Raviart elements. The original definition in the seminal paper by M. Crouzeix and P.-A. Raviart in 1973 [Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 7 (1973), pp. 33–75] is implicit and also contains substantial freedom for a concrete choice. In this paper, we introduce basic Crouzeix-Raviart spaces in 3D in analogy to the 2D case in a fully explicit way. We prove that this basic Crouzeix-Raviart element for the Stokes equation is inf-sup stable for polynomial degree k=2 (quadratic velocity approximation). We identify spurious pressure modes for the conforming \left (k,k-1\right) 3D Stokes element and show that these are eliminated by using the basic Crouzeix-Raviart space. [ABSTRACT FROM AUTHOR]