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

[Justin Chang]

Jed,

I am not quite sure what you're asking for. Are you asking for how people
actually implement this augmented TH? In other words, how the shape/basis
functions for this mixed function space would look? I have only seen in
some key note lectures and presentations at conferences briefly mentioning
this P2/(P1+P0) element, as if it's the de facto discretization for Stokes
flows. That said, even I am not too sure how this would look.

Matt,

In the 'quad_q2p1_full' example you pointed me to, is that P2/P1_disc or
P2/(P1+P0)? I imagine those are two very different discretizations, so when
you have the command line option "-pres_petscdualspace_lagrange_continuity
0" it looks to me you're doing the former?

Thanks,
Justin

On Mon, Jun 1, 2015 at 10:02 AM, Matthew Knepley <knepley at gmail.com> wrote:

> On Mon, Jun 1, 2015 at 9:38 AM, Jed Brown <jed at jedbrown.org> wrote:
>
>> Justin Chang <jychang48 at gmail.com> writes:
>>
>> > There are a few papers that discuss this modified/augmented Taylor-Hood
>> > elements for Stokes equations in detail (e.g.,
>> > http://link.springer.com/article/10.1007%2Fs10915-011-9549-4).
>>
>> This analysis does not state a finite element.
>
>
> They certaiinly state the approximation space up front. Then later in the
> paper
> they say that they independently test with P1 and P0, and that this has a
> 1D
> null space, and then in the solution section they have some way of
> handling that
> which I ignored because its easy to handle.
>
>   Matt
>
>
>> > From what I have seem, it seems people primarily use this to ensure
>> > local mass conservation while attaining the desirable qualities of the
>> > TH element.  Lately I have seen this element used in many FEniCS and
>> > Deal.II applications (and it's also very easy to implement, just a few
>> > additional lines of code),
>>
>> Could you point to a specific example?  How are they handling
>> linear dependence of the "basis"?
>>
>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
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