Correction to : J. Math. Fluid Mech. (2023) 25:64 https://doi.org/10.1007/s00021-023-00807-6

In the original publication of the article, the corrections team has missed to make the changes to the captions of the Figures 9 & 10 and missed to swap them both before the article was processed for publication.

The correct captions and their respective figures are as shown below:

Fig. 9
figure 1

Benchmark 3: Lift coefficient on different mesh levels computed in terms of volume integral as proposed in [17]

Fig. 10
figure 2

Navier-Stokes problem for \(U_0 = 1.5\), \(\mu = 10^{-3}\), and \(\delta t^{-1} = 25 \cdot 2^{\textrm{lvl}}\): Nonlinear convergence behavior of solvers using hierarchical starting procedure in space and time

The original article has been updated.