Error analysis of a time-splitting method for incompressible flows with variable density

Abstract

This work is devoted to obtain optimal temporal error estimates for a first-order time-splitting scheme for solving the incompressible Navier-Stokes equations with variable density. This scheme was firstly proposed by Li, Mei et al. (2013) [9]. First-order convergence rates have been numerically observed, but never hitherto proved. In this work, we will give a rigorous temporal error analysis for this scheme under some regularity assumptions.