This paper deals with a finite element method to solve fluid-structure
interaction problems.
More precisely it concerns the numerical computation of harmonic
hydroelastic vibrations under gravity.
It is based on a displacement formulation for both the fluid and the solid.
Gravity effects are included on the free surface of the fluid as well
as on the liquid-solid interface.
The pressure of the fluid is used as a variable for the theoretical
analysis leading to a well posed mixed linear eigenvalue problem.
Lowest order triangular Raviart-Thomas elements are used for the
fluid and classical piecewise linear elements for the solid.
Transmission conditions at the fluid-solid interface are taken into
account in a weak sense yielding a non conforming discretization.
The method does not present spurious or circulation modes for
nonzero frequencies.
Convergence is proved and optimal error estimates are given.
Finally, numerical results are shown.