Carlos Garcia, Gabriel N. Gatica, Salim Meddahi:
Finite element analysis of a pressure-stress formulation for the time-domain fluid-structure interaction problem
We present a convergence analysis for the space discretization of a time-dependent system of partial differential equations modeling an elasto-acoustic interaction problem. We use the Arnold-Falk-Winther mixed finite element method with weak symmetry in the solid and the usual Lagrange finite element method in the acoustic medium. The error analysis of the resulting global semi-discrete scheme relies essentially on the mapping properties of an adequate projector. We show that the method is stable uniformly with respect to the space discretization parameter and the Poisson modulus and we prove asymptotic error estimates.