ere $\phi'(x,z) \in \mathcal{V}$, $\bar \phi(x) \in \mathcal{W}$ as well as $\bar{P}(x) \in \mathcal{W}$ are the unknowns and $\psi' \in \mathcal{V}$, $\bar \psi \in \mathcal{W}$ and $ \bar{Q} \in \mathcal{W}$ the test functions.