Error estimates of a decoupled algorithm for a fluid-fluid interaction problem

In this paper, we study the error estimates of a decoupled algorithm for the fluid-fluid model. The system consists of two Navier-Stokes equations which are coupled by a set of linear interface conditions. We apply the partitioned time stepping method to decouple the system. The corresponding scheme is unconditionally stable and we prove that the error estimates for velocities in L2 norm are optimal. Moreover, under a restriction on the time step scale, we prove that the convergent orders for the velocities in H1 norm and for the pressures in L2 norm are Δt78+h and Δt34+h, respectively. Two numerical examples are given to verify our theoretical results. Besides, by comparing the decoupled algorithm with the coupled one, numerical test shows the effectiveness of our decoupled method.