Cohen structure theorem for completions at non maximal ideals

Question

Let $X=\textrm{Spec}(R)$ be a smooth affine local variety over $k$, an algebraically closed field of characteristic $0$, and let $u\in R$ be an element such that the divisor $\textrm{Spec}(R/(u))$ is smooth. Let $\hat{R}_u$ be the completion of $R$ with respect to the ideal $(u)$. Is $\hat{R}_u$ isomorphic to $R/(u)[[t]]$ ?(here $t$ is an indeterminate)