Fully Discrete Approximations to the Time-dependent Navier-Stokes Equations with a Projection Method in Time and Grad-div Stabilization (vol 80, pg 1330, 2019)

The proof of Lemma 5 in de Frutos et al. (J Sci Comput 80: 1330-1368, 2019) is not correct. An alternative statement of Lemma 5 and its proof is provided. With this new statement the order of convergence of the pressure is reduced by one half order in the spatial mesh size. Changes in the results relying Lemma 5 are also provided.

Automated summary

The proof of Lemma 5 in the study by de Frutos et al. (J Sci Comput 80: 1330-1368, 2019) is found to be incorrect, leading to an alternative statement and proof for Lemma 5. The new statement results in a halving of the convergence order of pressure in spatial mesh size, with corresponding changes in results relying on Lemma 5.