An algorithm for approximation of an unsteady fluid-structure interaction problem isproposed. The fluid is governed by the Navier-Stokes equations with boundary conditionson pressure, while for the structure a particular plate model is used. The algorithm is based on the modal decomposition and the Newmark Method for the structure and on the Arbitrary Lagrangian Eulerian coordinates and the Finite Element Method for the fluid.In this paper, the continuity of the stresses at the interface was treated by theLeast Squares Method. At each time step we have to solve an optimization problemwhich permits us to use moderate time step. This is the main advantage of this approach. In order to solve the optimization problem, we have employed the Broyden, Fletcher, Goldforb, Shano Method wherethe gradient of the cost function was approached by the Finite Difference Method.Numerical results are presented.
