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

[Matthew Knepley]

On Mon, Jun 1, 2015 at 9:51 PM, Justin Chang <jychang48 at gmail.com> wrote:

> 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?
>

Its Q2-P1_disc. That is stable and captures the pressure jumps well. This
is the standard variable-viscosity Stokes element in
my experience.

  Thanks,

     Matt


> 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
>>
>
>


-- 
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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