Numerical analysis for a chemotaxis-Navier–Stokes system Abelardo Duarte-Rodríguez, María Ángeles Rodríguez-Bellido, Diego A. Rueda-Gómez and Élder J. Villamizar-Roa ESAIM: M2AN, 55 (2021) S417-S445 Published online: 26 February 2021 DOI: 10.1051/m2an/2020039