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

[Jed Brown]

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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