  We consider the well-posedness and a priori error estimates of a 3d FEM-BEM
coupling method for fluid-structure interaction in the time domain. For an
elastic body immersed in a fluid, the exterior linear wave equation for the
fluid is reduced to an integral equation on the boundary involving the
Poincar\'{e}-Steklov operator. The resulting problem is solved using a Galerkin
boundary element method in the time domain, coupled to a finite element method
for the Lam\'{e} equation inside the elastic body. Based on ideas from the
time-independent coupling formulation, we obtain an a priori error estimate and
discuss the implementation of the proposed method. Numerical experiments
illustrate the performance of our scheme for model problems.
