SUPG stabilization of the steady advection-diffusion-reaction equation

Strong form

\[\begin{split} \begin{align*} &\text{Find}~u(\textbf{x}): \Omega \to \mathbb{R}~\text{such that} \\ &\mathbb{IBVP}\begin{cases} \textbf{a}\cdot\nabla u= \nabla\cdot(\mathsf{D}\cdot\nabla u) + Ru + J & \forall\textbf{x}\in\Omega \\ u=u_{\text{D}} & \forall \textbf{x}\in\partial\Omega_{\text{D}} \\ \textbf{n}\cdot(\mathsf{D}\cdot\nabla{u}) = u_{\text{N}} & \forall\textbf{x}\in\partial\Omega_{\text{N}}=\partial\Omega/\partial\Omega_{\text{D}} \end{cases}~. \end{align*} \end{split}\]

Weak form

\[\begin{split} \begin{align*} &\text{Find}~u\in V ~\text{such that} \\ &F(u,v)+F_{\text{SUPG}}(u,v)=0 \quad\forall v\in V~. \end{align*} \end{split}\]

stabilization term $\( F_{\text{SUPG}}(u,v)=... \)$