dolfin team mailing list archive

[kent-and@xxxxxxxxx]

>> 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
>

I think there are three ways to do this:
1) Remove the dofs that are constrained (i.e. v on boundary)
    This can be done by slicing matrices and vectors in an appropriate way.
    I guess it would be easy in Matlab, but not (yet) in fenics ?
2) Use a penalty term, as Johan says, this introduces an extra parameter
    in front of the penalty term.
3) Use Lagrange multipliers to impose the constraint, which leads to a larger
    system to solve.


Kent