  Let $F_{\wp}$ be a finite extension of $\mathbb{Q}_p$. By considering
partially de Rham families, we establish a Colmez-Greenberg-Stevens formula (on
Fontaine-Mazur $\mathcal{L}$-invariants) for (general) $2$-dimensional
semi-stable non-crystalline
$\mathrm{Gal}(\overline{\mathbb{Q}_p}/F_{\wp})$-representations. As an
application, we prove local-global compatibility results for completed
cohomology of quaternion Shimura curves, and in particular the equality of
Fontaine-Mazur $\mathcal{L}$-invariants and Breuil's $\mathcal{L}$-invariants,
in critical case.
