Finite element approximation of a displacement formulation for time-domain elastoacoustic vibrations

This paper deals with the numerical solution of a system of second-order in time partial differential equations modeling the vibrations of a coupling between an elastic solid and an inviscid compressible fluid. Both media are described in terms of their respective displacement fields. The problem is solved in the time domain by combining a Newmarkʹs scheme for time discretization with a finite element method for space discretization. The latter combines standard Lagrangian elements in the solid with lowest-order Raviart–Thomas elements in the fluid. Stability is proved and numerical results showing the good behavior of the method are reported.