  Let $R$ be the henselization of a local ring of a semistable family over the
spectrum of a discrete valuation ring of mixed characteristic $(0, p)$ and $k$
the residue field of $R$. In this paper, we prove an isomorphism of \'{e}tale
hypercohomology groups $\operatorname{H}^{n+1}_{\mathrm{\acute{e}t}}(R,
\mathfrak{T}_{r}(n)) \simeq \operatorname{H}^{1}_{\mathrm{\acute{e}t}}(k,
W_{r}\Omega_{\log}^{n})$ for any integers $n\geq 0$ and $r>0$ where
$\mathfrak{T}_{r}(n)$ is the $p$-adic Tate twist and $W_{r}\Omega_{\log}^{n}$
is the logarithmic Hodge-Witt sheaf. As an application, we prove the
local-global principle for Galois cohomology groups over function fields of
curves over an excellent henselian discrete valuation ring of mixed
characteristic.
