Sorry about the late reply. The issue that we require both u.n = 0 and \phi.n =0 , as there are fluxes on both the velocity and the test functions. Both boundary conditions are required to preserve the skew-symmetry of the Poisson bracket. I am currently implementing the velocity boundary in a strong sense, how would I go about implementing it weakly? Will ________________________________________ From: firedrake-bounces@imperial.ac.uk <firedrake-bounces@imperial.ac.uk> on behalf of Lawrence Mitchell <lawrence.mitchell@imperial.ac.uk> Sent: 18 February 2016 11:08 To: firedrake@imperial.ac.uk Subject: Re: [firedrake] Restricting a test function space On 18/02/16 11:01, William Booker wrote:
Dear all,
Hopefully this will help provide a bit more context for the problem.
OK, so you have a space (L^2)^3 on which you would like to impose u.n=0 on the boundary of the domain. As David says, in general, we can't lift the appropriate boundary nodes because the vector field normal to the boundary does not correspond to particular degrees of freedom. Can you instead enforce your boundary condition weakly, by requiring that \int u.n ds vanishes? In general in fully discontinuous spaces, it makes more sense to impose the boundary conditions weakly rather than strongly (after all, none of the nodes are topologically associated with the boundary anyway). Cheers, Lawrence