dolfin team mailing list archive

["Garth N. Wells" <gnw20@xxxxxxxxx>]

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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