Eigenvalue and eigenfunction error estimates for finite element formulations of linear hydroelasticity

Convergence of an approximate method for determining vibrational eigenpairs of an elastic solid containing an incompressible fluid is examined. The field variables are solid displacement and fluid pressure. We show that in suitable Sobolev spaces a variational formulation exists whose solution eigenvalues and eigenfunctions are identified with those of a compact operator. A nonconforming finite element approximation of this variational problem is described and optimal a priori error estimates are obtained for both the eigenvalues and eigenfunctions.