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[Shawn Walker <walker@xxxxxxxxxxxxxxx>]

Here are the bilinear forms:

a(u,X;v,Y) = (u,v) + <d_t X, d_t Y>

b(q,/mu;v,Y) = -(p,div(v)) + <\mu,v.n> - </mu,Y.n>

F(v,Y) = -<E,v.n>

G(q,\mu) = </mu,X.n>

where d_t is the tangential derivative, and <,> is an inner product on the 
boundary.  F and G are given data.

The mixed form is:

a(u,X;v,Y) + b(p,K;v,Y) = F(v,Y),   for all (v,Y)
b(q,/mu;u,X)            = G(q,\mu), for all (q,\mu)

where u and v are BDM contained in H(div),    X and Y are piecewise linear 
continuous on the boundary (in H^1(\Gamma)).  q and p is just pressure in 
L^2.  /mu and K is piecewise linear continuous in H^{1/2}(\Gamma).  The 
continuous system is well-posed; the discrete version is still to be 
checked.  BTW: I was wrong; I cannot use piecewise constants here.

This formulation comes from a semi-implicit discretization of Hele-Shaw 
flow with surface-tension.  I don't want to go into the details because it 
would take too much time.

So, I thought I would try and do this in DOLFIN.   But that seems 
difficult.  :(

- Shawn