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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the inf-sup stability of Crouzeix-Raviart Stokes elements in 3D
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by Stefan Sauter and Céline Torres HTML | PDF
Math. Comp. 92 (2023), 1033-1059 Request permission


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.

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Additional Information
  • Stefan Sauter
  • Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstr 190, CH-8057 Zürich, Switzerland
  • MR Author ID: 313335
  • Email:
  • Céline Torres
  • Affiliation: Department of Mathematics, University of Maryland, 4176 Campus Drive - William E. Kirwan Hall, College Park, Maryland 20742
  • ORCID: 0000-0001-9654-7438
  • Email:
  • Received by editor(s): May 1, 2022
  • Received by editor(s) in revised form: July 22, 2022
  • Published electronically: November 30, 2022
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 92 (2023), 1033-1059
  • MSC (2020): Primary 65N30, 65N12, 76D07, 33C45
  • DOI:
  • MathSciNet review: 4550319