For a ring $A$ and $f\in A$ a non-zero divisor, Beauville- Laszlo theorem gives a gluing statement for vector bundles on A in terms of a vector bundle on $A[\frac{1}{f}]$, a vector bundle on $\hat{A}$ the $(f)$-adic completion of $A$ and an isomorphism on $\hat{A}[\frac{1}{f}]$.

Is there a similar statement for a scheme $X$ and an effective Cartier divisor $D\subset X$?

For a commutative ring $A$ and $f\in A$ a non-zero divisor, the Beauville-Laszlo theorem gives a gluing statement for vector bundles on $A$ in terms of a vector bundle on $A\big[\frac{1}{f}\big]$, a vector bundle on $\hat{A}$ the ($f$)-adic completion of $A$ and an isomorphism on $\hat{A}\big[\frac{1}{f}\big]$.

Is there a similar statement for a scheme $X$ and an effective Cartier divisor $D\subset X$?