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

[Justin Chang]

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.

On Sat, May 30, 2015 at 8:28 PM, Jed Brown <jed at jedbrown.org> wrote:

> Justin Chang <jychang48 at gmail.com> writes:
>
> > Hello everyone,
> >
> > In SNES ex62, it seems to solve the Stokes equation using TH elements
> > (i.e., using P2-P1 elements). However, this formulation is not locally
> > conservative, and as a result many people use the P2-P1/P0 elements where
> > the pressure space is enriched with a piece-wise constant to ensure mass
> > conservation at the element level.
>
> 1. P2-P1disc is not stable.
>
> 2. P1disc is not "P1 enriched with piecewise constant", and the latter
> does not make sense.
>
> 3. You're probably thinking of the Crouzeix-Raviart element, which has
> P1disc pressure and P2 enriched with a cubic bubble for velocity.  That
> element is stable and locally conservative.
>
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