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
_______________________________________________
DOLFIN-dev mailing list
[email protected]
http://www.fenics.org/mailman/listinfo/dolfin-dev
