Finite element analysis for a Herrmann pressure formulation of the elastoacoustic problem with variable coefficients

In two and three dimensions, this study is focused on the numerical analysis of an eigenproblem associated with a fluid-structure model for sloshing and elasto-acoustic vibration. We use a displacement-Herrmann pressure formulation for the solid, while for the fluid, a pure displacement formulation is considered. Under this approach we propose a non conforming locking-free method based on classic finite elements to approximate the natural frequencies (of the eigenmodes) of the coupled system. Employing the theory for non-compact operators we prove convergence and error estimates. Also we propose an a posteriori error estimator for this coupled problem which is shown to be efficient and reliable. All the presented theory is contrasted with a set of numerical tests in 2D and 3D.