Numerical Approximation of an Axisymmetric Elastoacoustic Eigenvalue Problem

. This paper deals with the numerical approximation of a pressure/displacement formulation of the elastoacoustic vibration problem in the axisymmetric case. We propose and analyze a discretization based on Lagrangian finite elements in the fluid and solid domains. We show that the scheme provides a correct approximation of the spectrum and prove quasi-optimal error estimates. We report numerical results to validate the proposed methodology for elastoacoustic vibrations.