integral boundary conditions

Does "const." mean "Q_{ij}" with known values for Q_{ij}?

Yes, of course, I meant there's known tensor on the right hand side, so the BC is:

\int_{\Gamma} {(u_i n_j + u_j n_i) d\Gamma} = Q_{ij}

Regards,
Marek

You are right: Your secondary condition cannot be applied directly in escript.

One needs to bring in a Lagrange multiplier: If the original PDE in weak form is given as [v,u]=<f,v> with
right hand side f, solution u, test functions v and appropriate inner products [,] and <,> then the modified equation is given as [v,u] + \sum_ij lambda_ij {g_ij,v} =<f,v> with Lagrange multipliers lambda_ij, and an (semidefinite) bilinear form {.,.} with {g_ij,u}=Q_ij.

There are a few ways this can be solved. From my point of few the most robust is the following:

We solve the following (3x3+1) equations (using escript):

 [v,z_0] =<f,v>
 [v,z_ij] = - {g_ij,v}

(assuming that these problems have a unique solution!!!). We then set u = z_0 + \sum_ij lambda_ij z_ij
then we have: [v,u] + \sum_ij lambda_ij {g_ij,v} =<f,v> and need to find lambda_ij. In fact we have
Q_ij = {g_ij,u}= { g_ij, z_0} + \sum_kl lambda_kl { g_ij, z_kl }
which is a system of 9 equations with 9 unknowns (in 3D) (use numpy). Not that -{ g_ij, z_kl }= [z_kl,z_ij] so the coefficient matrix is SPD if [.,.] is elliptic.

Hope this makes sense.