Error analysis of a fully discrete consistent splitting MAC scheme for time dependent Stokes equations

Abstract

We construct and analyze a numerical scheme based on the truly consistent splitting approach in time and the MAC discretization in space for the time dependent Stokes equations. The scheme only requires solving several Poisson type equations for the velocity and pressure at each time step. We establish the equivalence between two different formulations of the fully discrete consistent splitting schemes, prove unconditional stability, and establish first-order in time and second-order in space error estimates for velocity and pressure in different discrete norms. We also provide numerical experiments to verify our theoretical results.