On Mon, 20 Apr 2009, Anders Logg wrote:

> On Thu, Apr 16, 2009 at 09:19:51PM -0400, Shawn Walker wrote:
>>
>> On Fri, 17 Apr 2009, Garth N. Wells wrote:
>>
>>> [email protected] wrote:
>>>> I would also like this capability! It is  something that often shows up
>>>> in inverse/optimal control problems.
>>>>
>>>> Written in FFC/UFL your first equation reads:
>>>>
>>>> dot(u,v)*dx - p*div(v)*dx + lmbda*dot(v,n)*ds
>>>>
>>>> where u, p, lmbda are trial functions.
>>>>
>>>> You could form one system or create a block matrix. Anyhow
>>>> the term
>>>>   lmbda*dot(v,n)*ds
>>>> would lead to a matrix with a very big kernel since you are not able to
>>>> restrict the dofs of lmbda only to the boundary.
>>>>
>>>> What you can currently do is to restrict the functionspace for lmbda to
>>>> all the cells
>>>> associated with the boundary.
>>>>
>>>> Using restricted functionspaces (in a simpler fashion) can be found in
>>>> demo/function/restriction.
>>>>
>>>> The restriction does only work on cells for now.
>>>>
>>>> We could discuss Uzawa and/or block matrices for this problem but I think
>>>> the simplest start is to create one system to begin with.
>>>>
>>>> Whether it makes sense that lmbda lives on the whole cell associated with
>>>> the boundary, I don't know.
>>>>
>>>
>>> It should live only on the boundary. In practice this only becomes an
>>> issue for higher-order elements with internal dofs.
>>>
>>> Garth
>>
>> Yes, I agree.
>>
>> So how ridiculous is it to enable FFC/DOLFIN to have finite element
>> functions that are only defined on the boundary of the domain?  I'm
>> guessing there would be some special DoFmappings to go from the global
>> domain numbering to a boundary numbering only.  This would be really nice
>> to have.  There are lots of cases in practice that have these kinds of
>> boundary functions.
>>
>> - Shawn
>
> It's not impossible but it requires some thought. I think Garth has
> asked about this for a long time as well (to have function spaces that
> only live on facets). I don't really know how to best handle it.
>
> -- 
> Anders

ok.  I just implemented what I needed in MATLAB and that formulation 
works.  But it would certainly be great to have it in FENICS.

- Shawn
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