t_{e_{i, j}} \boldsymbol{u} \cdot \boldsymbol{n}_{i, j}\left(\lambda_{i}-\lambda_{j}\right) \, ds,$$<p>where $n_i = t_i^{\bot}$ is the rotation of the unit tangential vector of $e_i$ by $90^{\deg}$ counterclockwise. Note that both the bases and the dual bases depend on the orientation of the edge not necessiliarly couterclockwise.</p>
<p>It is straightforward to verify the "orthogonality":
$$d^{\phi}(\psi) = 0, \quad d^{\psi}(\phi) = 0, \quad d_i^{\phi}(\phi_j) = \delta_{ij}, \quad  d_i^{\psi}(\psi_j) = \de