The Equivalence of Standard and Mixed Finite Element Methods in Applications to Elasto-Acoustic Interaction

Two commonly used problem formulations for the description of acoustic wave propagation are investigated; one is based on fluid displacement, and the other one is based on the velocity potential as the primary variable. Their equivalence under general Neumann boundary conditions is shown on both the continuous and the discrete level. To obtain the equivalence in the discrete setting, a nonstandard mixed finite element formulation is introduced. Thus, the transfer of an already available analysis for coupled elasto-acoustic problems in the displacement formulation to the potential formulation can be achieved. For the applications, the potential formulation is of special interest because it allows the use of standard Lagrangian elements in both the structure and the fluid subdomain. Moreover, the approach does not require any conformity of the subdomain meshes at the interface, which considerably simplifies the physics-adapted mesh generation. Several engineering examples demonstrate the applicability and efficiency of the resulting numerical scheme.