Finite element analysis for a pressure–stress formulation of a fluid–structure interaction spectral problem

The aim of this paper is to analyze an elastoacoustic vibration problem employing a dual-mixed formulation in the solid domain. The Cauchy stress tensor and the rotation are the primary variables in the elastic structure while the standard pressure formulation is considered in the acoustic fluid. The resulting mixed eigenvalue problem is approximated by a conforming Galerkin scheme based on the lowest order Lagrange and Arnold–Falk–Winther finite element subspaces in the fluid and solid domains, respectively. We show that the scheme provides a correct approximation of the spectrum and prove quasi-optimal error estimates. Finally, we report some numerical experiments.