\right\}}_F &  = v^+,
      \\
      {\llbracket {\mathbf{n}}\times{\mathbf{v}}\rrbracket}_F &  = {\mathbf{n}}^+ \times{\mathbf{v}}^+, \\
       {\llbracket {\mathbf{n}}\cdot{\mathbf{v}}\rrbracket}_F & = {\mathbf{n}}^+ \cdot{\mathbf{v}}^+,
      \\
      {\llbracket v{\mathbf{t}}\rrbracket}_F & = v^+ {\mathbf{t}}^+.
    \end{aligned}
  \right .$$ Let $\mathbb{P}_p(D)$ denote the space of polynomial functions of degree at most $p$ on a domain $D$. For any element $K\in{\mathcal{T}}_h$, let $V^p(K)$ be the space $\mathbb{P}_p(K)$ and ${\mathbf{V}}^p(K)$ the space $(\mathbb{P}_p(K))^2$. The discontinuous finite element spaces are then defined by $$\label{eq:dgSpace}
  \begin{aligned}
    V^p_h & = \left\{ v \in L^{2}(\Omega) \ \lvert \ v|_K\in
    V^p(K), \ \forall K\in{\mathcal{T}}_h\right\},
    \\
    {\mathbf{V}}^p_h & = \left\{ {\mathbf{v}}\in (L^2(\Omega))^2 \ \lvert \
    {\mathbf{v}}|_K\in {\mathbf{V}}^p(K), \ \forall K\in{\mathcal{T}}_h \right\},
  \end{aligned}$$ where $L^2(\Omega)$ is the space of square integrable functions on the domain $\Omega$. We also introduce a traced finite element space $$\label{SpaceM}
M^p_h = \left\{ \eta \in L^2({\mathcal{F}}_h) \ \lvert
  \ \eta|_F \in\mathbb{P}_p(F),
  \ \forall F\in{\mathcal{F}}_h  \right\}.$$ Note that $M^p_h$ consists of functions which are continuous on an edge, but discontinuous at its ends. The restrictions of $V^p_h$, ${\mathbf{V}}^p_h$ and $M^p_h$ in $\Omega_S$ are denoted by $\widetilde{V}^p_h$, $\widetilde{{\mathbf{V}}}^p_h$ and $\widetilde{M}^p_h$. For two vectorial functions $\mathbf{u}$ and ${\mathbf{v}}$ in $(L^2(D))^2$, we introduce the inner product $(\mathbf{u},{\mathbf{v}})_{D}   =   {\displaystyle}\int_D\mathbf{u}\cdot\overline{{\mathbf{v}}}  \,  {\rm d}x$, where $\overline{\cdot}$ denotes the complex conjugation. Likewise 