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The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems. (English) Zbl 0853.65111
Summary: We prove a double order for the convergence of eigenfrequencies in fluid-structure vibration problems. We improve estimates given recently for compressible and incompressible fluids. To do this, we extend classical results on finite element spectral approximation to nonconforming methods for noncompact operators.

MSC:
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
70J30 Free motions in linear vibration theory
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Q05 Hydro- and aero-acoustics
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