dolfin team mailing list archive

["Johan Hoffman" <jhoffman@xxxxxxxxxx>]

> 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)?

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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