[petsc-users] Modified Taylor-Hood elements with piece-wise constant pressure for Stokes equation

[Jed Brown]

Justin Chang <jychang48 at gmail.com> writes:

> I am referring to P2 / (P1 + P0) elements, I think this is the correct way
> of expressing it. Some call it modified Taylor Hood, others call it
> something else, but it's not Crouzeix-Raviart elements.

Okay, thanks.  This pressure space is not a disjoint union (the constant
exists in both spaces) and thus the obvious "basis" is actually not
linearly independent.  I presume that people using this element do some
"pinning" (like set one cell "average" to zero) instead of enforcing a
unique expression via a Lagrange multiplier (which would involve a dense
row and column).  That may contribute to ill conditioning and in any
case, would make domain decomposition or multigrid preconditioners more
technical.  Do you know of anything explaining why the method is not
very widely used (e.g., in popular software packages, finite element
books, etc.)?
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