[Libmesh-users] Boundary conditions via Lagrange multipliers ?

[John P. <pet...@cf...>]

Michael Schindler writes:
 > Hello,
 > 
 > I am trying to implement boundary conditions (for the Navier-Stokes
 > equation of example 13) via Lagrange multipliers.
 > 
 > For this I need extra degrees-of-freedom for every boundary-side of an
 > element.
 > One possibility, that already works, is to define an extra variable.
 > But this has then DOFs at all elements of the mesh -- far too many.
 > This makes the System unnecessary large.
 > 
 > Therefore, I would like to know:
 > 
 > 1. Is there a ready-made way to implement Lagrange multipliers?
 > or
 > 2. Can I "throw away" DOFs of one specified variable where I do not
 >    want to calculate its solution?
 > 3. Can I add DOFs to a System without adding a variable?

Hi,

Yes that seems like a reasonable and general thing to have.  I hope
Ben will comment on this, since he was working with a constrained
system at some point in which he only activated the extra DOF on
elements which required it.  In that case, I believe the lagrange
multiplier was used to enforce positivity of the solution in each
element...

-John