ffc team mailing list archive

[Shawn Walker <walker@xxxxxxxxxxxxxxx>]

Actually, let me write out the full system:

(u,v) - (p,div(v)) + < \lambda,v.n > = 0, for all v
-(q,div(u)) = 0, for all q
<\mu,u.n> = <\mu,g>, for all /mu

note: <,> is an inner product on the boundary.

So it is a saddle point system with multiplier \lambda on the boundary 
only.  The only way I know to define this in FFC will create a \lambda 
that is defined everywhere, and I don't want that.  So, is there a way to 
do this?  This is not the exact problem that I want to solve, but 
something similar.

- Shawn

On Thu, 16 Apr 2009, Jed Brown wrote:

> On Thu 2009-04-16 19:45, Anders Logg wrote:
> > On Thu, Apr 16, 2009 at 10:42:08AM -0400, Shawn Walker wrote:
> > > Hello.
> > >
> > > I was wondering how do you have finite element spaces that only live on
> > > the boundary?  Say I want to solve a mixed form for Laplace's equation.
> > > And, I would like to set the normal flux on the boundary by using a
> > > Lagrange multiplier that is only defined on the boundary.  Is there an
> > > example on this already?
> >
> > Is it not enough to add a boundary integral? Something like
> >
> >   lmbda*(dot(sigma, n) - g)*ds
>
> You seem to be describing a penalty method which doesn't add any dofs
> and can be enforced this way (just choose 'lmbda' to be a big number).
> The issue is that lmbda needs to have a suitable number of degrees of
> freedom in the global system and these need to correspond to basis
> functions on the boundary.
>
> Jed