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A mistake for Crouzeix–Falk element #472
Description
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A clear and concise description of what the bug is, which element(s) it relates to.
By the article Crouzeix–Falk, the basis functions seem to be continuous in the Gauss point in the triangle sides, instead of in the midpoint and two three equal points.
Additional context
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More information can see the article.
Nonconforming finite elements for the Stokes problem.pdf
Crouzeix, Michel and Falk, Richard S. Nonconforming finite elements for the Stokes problem, Mathematics of Computation 52, 437–456, 1989. [DOI: 10.2307/2008475] [BibTeX]
Activity
mscroggs commentedon Nov 18, 2025
From https://defelement.org/elements/examples/triangle-crouzeix-falk-3.html, you can see that the points are 1/4, 1/2 and 3/4 of the way along the edge - ie equally spaced. Is this error appearing somewhere else?
Lu-wei-sleep commentedon Nov 18, 2025
mscroggs commentedon Nov 18, 2025
The website says they are point evaluations at (3/4,1/4), (1/2,1/2), (1/4,3/4) on edge 0, (0,1/4), (0, 1/2), (0, 3/4) on edge 1, (1/4, 0), (1/2, 0), (3/4, 0) on edge 2 and (1/3, 1/3) on the interior of the cell. Which of these are wrong?
Lu-wei-sleep commentedon Nov 19, 2025
Please see the article Nonconforming finite elements for the Stokes problem.pdf. The dofs are in the guassian point of the cell.
mscroggs commentedon Nov 19, 2025
Oh I see. Sorry I misread what you wrote in your first message
jorgensd commentedon Aug 12, 2026
Bump as I just became aware of this