on the equation weighted by $w$, we arrive at the final form of the problem:
Find $(\mathbf{q}_h, u_h, \hat{u}_h) \in
\mathcal{V}_h^p \times \mathcal{W}_h^p \times \mathcal{M}_h^p$ such that
-@f{eqnarray*}
+@f{align*}
(\mathbf{v}, \kappa^{-1} \mathbf{q}_h)_{\mathcal{T}}
- ( \nabla\cdot\mathbf{v}, u_h)_{\mathcal{T}}
+ \left<\mathbf{v}\cdot\mathbf{n}, \hat{u}_h\right>_{\partial\mathcal{T}}
- &=& 0,
+ &= 0,
\quad &&\forall \mathbf{v} \in \mathcal{V}_h^p,
\\
- (\nabla w, \mathbf{c} u_h)_{\mathcal{T}}
+ (w, \nabla \cdot \mathbf{q}_h)_{\mathcal{T}}
+ (w, (\mathbf{c}\cdot\mathbf{n}) \hat{u}_H)_{\partial \mathcal{T}}
+ \left<w, \tau (u_h - \hat{u}_h)\right>_{\partial \mathcal{T}}
- &=&
+ &=
(w, f)_{\mathcal{T}},
\quad &&\forall w \in \mathcal{W}_h^p,
\\
\left< \mu, \hat{u}_h\mathbf{c} \cdot \mathbf{n}
+ \mathbf{q}_h\cdot \mathbf{n}
+ \tau (u_h - \hat{u}_h)\right>_{\partial \mathcal{T}}
- &=&
+ &=
\left<\mu, g_N\right>_{\partial\Omega_N},
\quad &&\forall \mu \in \mathcal{M}_h^p.
@f}