Convergence of a fluid–structure interaction problem decoupled by a Neumann control over a single time step

Building off of previous analytical results for recasting fluid–structure interaction into an optimal control setting, an a priori error estimate is given for the optimality system by means of BRR theory. The convergence of the steepest descent method is proven in a discrete setting for a sufficiently small time step and mesh size. A numerical study is included supporting the theoretical rate of convergence over a single time step. Additional results demonstrate optimal convergence in space and time over several time steps.