  In this work we analyze the stability and convergence properties of a
loosely-coupled scheme, called the kinematically coupled scheme, for
interaction between an incompressible viscous fluid and a thin structure. We
consider a benchmark problem where the structure is modeled using the linearly
elastic Koiter membrane model and the coupling between the fluid and structure
is linear. We derive the energy estimates associated with the unconditional
stability and, for the first time, present a priori estimates showing optimal,
first-order in time, convergence. The theoretical stability and convergence
results are supported with numerical examples.
