Error analysis of the immersed interface method for Stokes equations with an interface

The immersed interface method using the three Poisson equation approach has been successfully developed to solve incompressible Stokes equations with interfaces (Li, 2015 and Li and Ito, 2006). While the numerical results show second order convergence for both velocity and pressure, rigorous error analysis is still missing. Based on recent theoretical development, particularly the error analysis by Beale and Layton (2006), second order convergence has been shown in this paper for both pressure and velocity under some assumptions.