Hi everybody,
I am looking for a way to force zero flux (e.g. heat flux for the thermal problem) at a boundary with Lagrange multipliers.
Normally, the zero flux condition is only weakly fulfilled with a Neumann boundary condition. A common way to enforce zero flux is to use a mixed formulation with the flux as an additional primary variable (see this tutorial in legacy fenics). However, this would mean additional degrees of freedoms, which I would like to avoid.
Therefore, I am asking for a way to do this with Lagrange multipliers. How would the additional term in the variational problem look like? Furthermore, would it be possible to define the Lagrange multipliers only at the particular boundary where the zero-flux should be enforced?
Thank you for your help.
Original example problem: \nabla \cdot q = 0 with q = - \lambda \nabla T