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[Anders Logg <logg@xxxxxxxxx>]

On Fri, Jun 06, 2008 at 07:15:33PM -0700, Chong Luo wrote:
> Is it possible to specify test functions which are zero on the Dirichlet
> boundary?

No, you have to apply such constraints afterwards to the linear
system, using the DirichletBC class in DOLFIN.

> 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!

There is a demo that demonstrates how to implement the mixed Poisson
system in DOLFIN. Take a look in

  demo/pde/mixed-poisson/

This demo uses BDM1 elements for the flux and DG0 elements for the
pressure to get stability.

-- 
Anders

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