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[Robert Kirby <robert.c.kirby@xxxxxxxxx>]

A classic reference to this kind of situation is the "other" Raviart-Thomas
paper from 1977,
the one on "primal hybrid" methods in which you work with the primal rather
than mixed form
of Poisson, but enforce continuity by a Lagrange multiplier on edges rather
than by assembly
in the function space.

Interesting paper.

Rob

On Thu, Apr 16, 2009 at 12:59 PM, Anders Logg <logg@xxxxxxxxx> wrote:

> On Thu, Apr 16, 2009 at 07:56:32PM +0200, 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.
>
> ok, now I see what you mean.
>
> No, that's not possible to do (mixing function spaces on different
> meshes in the same formulation).
>
> --
> Anders
>
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