Hello,

I am trying to go through the NGSolve example 2.5 on the mixed formulation for the diffusion equation. The primal problem has the integral on the Neumann boundary defined as:

g*vp * ds.

Where is “ds” active? Is “ds” automatically defined on the complement of the essential boundary? For the primal problem the essential boundary is set by the flag: dirichlet=“bottom”. So would “ds” be active on the

“right|top|left” boundaries?

Similarly for the mixed formulation, the condition u=u_D is to be applied on the bottom edge, but this is done as part of the variational form. The equivalent NGSolve implementation is given in the example as:

ud*(tau.Trace()*normal)*ds.

For the mixed formulation, the Dirichlet boundary on the H(div) space is given as: dirichlet=“right|top|left”. So is “ds” automatically defined on the complement of this, which is the bottom edge?

Thank you,

Anand