Johan Hoffman wrote:
>> On Thu, Feb 07, 2008 at 05:43:13PM +0100, Marie Rognes wrote:
>>
>>> Anders Logg wrote:
>>>
>>>> On Thu, Feb 07, 2008 at 05:07:46PM +0100, Marie Rognes wrote:
>>>>
>>>>
>>>>> Hi,
>>>>>
>>>>> I would like to construct a vector-valued finite element space where
>>>>>
>>> the
>>>
>>>>> components may be related to each other on the boundary.
>>>>>
>>>>> Example:
>>>>>
>>>>> Let P1 be piecewise linears on K.
>>>>> I want the subspace {(u, v) \in P1 x P1 such that u = v on the
>>>>> boundary of K.}
>>>>>
>>>>> Is this possible in DOLFIN today?
>>>>>
>>>>>
>>>> Not that I know. Generally, we can't handle constraints.
>>>>
>>>>
>>>>
>>> Darn. How hard do you think it would be to set-up?
>>>
>> I don't know. There was some discussion a month back on setting
>> no-slip constraints (zero normal component on boundaries) which is
>> similar. I think the conclusion was that we didn't find a general
>> solution. (But most likely there is one...)
>>
>> --
>> Anders
>>
>
> I guess you could set it up as a penalty on (u-v)?
>
>
Pardon my ignorance please, but how does this work?
Is is typically well-posed?
--
Marie
> For the zero normal component case things are a little bit different,
> since then you use a local coordinate transormation of the test functions
> from Cartesian to normal-tangent coordinates, so that you can let the
> tanget direction be free but the normal direction constrained. This is
> planned to be part of the next release of Unicorn for linear (P1) vector
> elements. But as Anders says it is not evident how to extend this to
> general elements.
>
> /Johan
>
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>
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--
Marie E. Rognes
Ph.D Fellow,
Centre of Mathematics for Applications,
University of Oslo
http://folk.uio.no/meg
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