$k\geq 0$ and a domain $\mathcal O\subset \mathbb{R}^3$, ${\mathcal{P}}_k(\mathcal O)$ denotes the space of polynomials of degree at most $k$ on $\mathcal O$. For any $m\geq 1$, we introduce the finite element spaces $$\mathbf{X}_h := \prod_{K\in {\mathcal{T}}_h^{\Omega_C}} P_m(K)^3
 \quad \text{and} \quad
 V_h := \prod_{K\in {\mathcal{T}}_h^{\Omega_I}} \tilde{\mathcal{P}}_{m}(K),$$ where $$\label{tildePm}
 \tilde{\mathcal{P}}_{m}(K):=\begin{cases}
 {\mathcal{P}}_m(K) & \text{if $\partial K\cap \Gamma \notin {\mathcal{F}}_h^\Gamma$ }\\
 {\mathcal{P}}_m(K) + {\mathcal{P}}_{m+1}^T(K) & \text{if $T=\partial K\cap \Gamma \in {\mathcal{F}}_h^\Gamma$}
 \end{cases}$$ with ${\mathcal{P}}_{m+1}^T(K)$ representing the subspace of ${\mathcal{P}}_{m+1}(K)$ spanned by the elements of the Lagrange basis corresponding to nodal points located on $T$. It follows that ${\mathcal{P}}_m(K) \subset \tilde{\mathcal{P}}_m(K) \subset 
{\mathcal{P}}_{m+1}(K)$ and if $T = \partial K \cap \Gamma \in {\mathcal{F}}_h^\Gamma$ then $\tilde{\mathcal{P}}_m(K)|_T = {\mathcal{P}}_{m+1}(T)$.

Let $h_{\mathcal{F}}\in \prod_{F\in \mathcal{F}_h} {\mathcal{P}}_0(F)$ and $h_{\mathcal{E}}\in \prod_{e\in \mathcal{E}_h} {\mathcal{P}}_0(e)$ be defined by $h_{\mathcal{F}}|_F := h_F$ $, \forall F \in \mathcal{F}_h$ and $h_{\mathcal{E}}|_e := h_e$ $, \forall e \in {\mathcal{E}}_h$ respectively. By virtue of our hypotheses on $\sigma$ and on the triangulation ${\mathcal{T}}_h^{\Omega_C}$, we may consider that $\sigma$ is an element of $\prod_{K\in \mathcal{T}_h^{\Omega_C}} {\mathcal{P}}_0(K)$ and denote $\sigma_K:= \sigma|_K$ for all $K\in \mathcal{T}_h^{\Omega_C}$. We introduce $\mathtt{s}_{\mathcal{F}}\in \prod_{F\in \mathcal{F}_h(\Omega_C)} {\mathcal{P}}_0(F)$ defined by $\mathtt{s}_F := \min(\sigma_K, \sigma_{K'})$, if $F = \partial K \cap \partial K'\in {\mathcal{F}}_h^0(\Omega_C)$ and $\mathtt{s}_F := 