dolfin team mailing list archive

[Marie Rognes <meg@xxxxxxxxxxx>]

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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--
Marie E. Rognes
Ph.D Fellow, 
Centre of Mathematics for Applications, 
University of Oslo
http://folk.uio.no/meg