Hybrid finite element analysis of fluid-structure systems with coupling on curved interfaces

Abstract

This paper deals with a finite element approximation of the vibration modes of fluid–structure systems coupled on curved interfaces. It is based on a displacement formulation for both the fluid and the solid. Lowest order Raviart–Thomas elements are used for the fluid and standard continuous linear elements for the solid. Compatibility conditions are weakly imposed at a polygonal approximation of the fluid–solid interface by means of a Lagrange multiplier. Convergence, nonexistence of spurious or circulation nonzero frequency modes and optimal order error estimates for eigenfunctions/eigenvalues are proved. To do this, we use recent results about spectral approximations for noncompact operators to nonconforming hybrid finite element methods. The validity of a discrete compactness property for the discrete spaces considered here is also discussed.