  In fluid-structure interaction problems, some people use a penalty method for
positioning the structure inside the fluid. This is usually performed by
considering that the fluid is very stiff or/and very heavy at the place
occupied by the structure. These methods are very convenient for the
programming point of view but lead to ill conditioned operators. This is a
drawback in the numerical solution methods. In particular the forces applied to
the structure by the surrounding flow are not accurately estimated because the
penalty parameter -- which is a very large number -- appears in their
expressions. We suggest in this paper a mathematical analysis of the
difficulties encountered and we discuss how the penalty-duality method of D.
Bertsekas can be an interesting alternative to overcome them.
