## Preprint 2014-21

## Salim Meddahi, David Mora:

### Nonconforming mixed finite element approximation of a fluid-structure interaction spectral problem

### Abstract:

The aim of this paper is to analyze an elastoacoustic vibration problem formulated in terms of the Cauchy stress tensor and the fluid pressure as primary variables. The resulting eigenvalue problem is approximated by a non-conforming Galerkin scheme based on the lowest order Lagrange and Raviart-Thomas 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.

This preprint gave rise to the following definitive publication(s):

**Salim MEDDAHI, David MORA: ***Nonconforming mixed finite element approximation of a fluid-structure interaction spectral problem*. Discrete and Continuous Dynamical Systems - Series S, vol. 9, 1, pp. 269-287, (2016).