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
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