  Understanding quantum entanglement in interacting higher-dimensional
conformal field theories is a challenging task, as direct analytical
calculations are often impossible to perform. With holographic entanglement
entropy, calculations of entanglement entropy turn into a problem of finding
extremal surfaces in a curved spacetime, which we tackle with a numerical
finite-element approach. In this paper, we compute the entanglement entropy
between two half-spaces resulting from a local quench, triggered by a local
operator insertion in a CFT$_3$. We find that the growth of entanglement
entropy at early time agrees with the prediction from the first law, as long as
the conformal dimension $\Delta$ of the local operator is small. Within the
limited time region that we can probe numerically, we observe deviations from
the first law and a transition to sub-linear growth at later time. In
particular, the time dependence at large $\Delta$ shows qualitative differences
to the simple logarithmic time dependence familiar from the CFT$_2$ case. We
hope that our work will motivate further studies, both numerical and
analytical, on entanglement entropy in higher dimensions.
