[firedrake] RT/BDM works but not TH/VMS

[Justin Chang]

V = VectorFunctionSpace(mesh,"CG",1)
Q = FunctionSpace(mesh,"CG",1)
W = V*Q
v,p = TrialFunctions(W)
w,q = TestFunctions(W)
...
a = (dot(v, w) - p*div(w) - div(v)*q)*dx + 0.5*dot(v+grad(p),w+grad(q))*dx
L = f*q*dx

if that's what you're asking

On Fri, Nov 13, 2015 at 1:48 PM, Colin Cotter <colin.cotter at imperial.ac.uk>
wrote:

> Hi Justin,
>   What is the form you are using for the VMS formulation?
>
> all the best
> --cjc
>
> On 13 November 2015 at 19:21, Justin Chang <jychang48 at gmail.com> wrote:
>
>> Hi all,
>>
>> So given this Darcy problem:
>>
>>   a = (dot(v, w) - p*div(w) - div(v)*q)*dx
>>   L = f*q*dx
>>
>> where f = "12*pi*pi*sin(pi*x[0]*2)*sin(pi*x[1]*2)*sin(2*pi*x[2])" and
>> with these solver options:
>>
>> 'ksp_type': 'gmres',
>>     #'ksp_monitor_true_residual': True,
>>     'pc_type': 'fieldsplit',
>>     'pc_fieldsplit_type': 'schur',
>>     'pc_fieldsplit_schur_fact_type': 'upper',
>>     'pc_fieldsplit_schur_precondition': 'selfp',
>>     'fieldsplit_0_ksp_type': 'preonly',
>>     'fieldsplit_0_pc_type': 'bjacobi',
>>     'fieldsplit_0_sub_pc_type': 'ilu',
>>     'fieldsplit_1_ksp_type': 'preonly',
>>     'fieldsplit_1_pc_type': 'hypre',
>>     'fieldsplit_1_pc_hypre_type': 'boomerang'
>>
>> And without specifying any boundaries (my forcing function f is chosen so
>> that the pressure is homogeneous on the boundary), RT0 and BDM works
>> beautifully.
>>
>> However, with Taylor-Hood elements and VMS (which is equal order CG1 plus
>> a least squares stabilization), the velocity works but the pressure
>> solution is screwed up.
>>
>> Why is that?
>>
>> Thanks,
>> Justin
>>
>
>
>
> --
> http://www.imperial.ac.uk/people/colin.cotter
>
> www.cambridge.org/9781107663916
>
>
>
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