Marie Rognes wrote:
> 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?
>
Take a look at
/src/demo/pde/dg/cpp/Poisson.form
It enforces u = 0 using Nitsche's method. If drop all the *ds terms except
gamma/h*v*u*ds
you'll get a penalty method.
> Is is typically well-posed?
>
Yes.
Garth
>
> --
> 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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>
>
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