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[Chong Luo <luo.chong@xxxxxxxxx>]

Is it possible to specify test functions which are zero on the Dirichlet boundary?

For example, let's say we want to use mixed finite element to solve Poisson's equation with both Neumann and Dirichlet boundary conditions:
- Laplace (p) = f  in Omega
p = pD on Gamma0
dp/dn = uN on Gamma1

So we introduce velocity u = - grad(p), and get the following mixed formulation:
(u, v) + (v, grad(p)) = 0                           for all v in X
(u, grad(q))  = -(f,q) + <q, uN>              for all q in M
where (,) is integration on Omega, while <,> is integration on the boundary of Omega.

I found that I need to take test function q such that q is zero on the Dirichlet boundary Gamma0 (which has to be nonempty), for this mixed formulation to satisfy LBB condition.  Is it possible to specify this constraint in FFC/FEniCS?

Thank you!

Best,
Chong Luo