A SPACE-TIME FINITE-ELEMENT METHOD FOR STRUCTURAL ACOUSTICS IN INFINITE DOMAINS .1. FORMULATION, STABILITY AND CONVERGENCE

A space-time finite element method for solution of the exterior struct ural acoustics problem involving the interaction of vibrating elastic structures submerged in an infinite acoustic fluid is formulated. In p articular, rime-discontinuous Galerkin and Galerkin Least-Squares (GLS ) variational formulations for coupled structural acoustics in unbound ed domains are developed and analyzed for stability and convergence. T he formulation employs a finite computational fluid domain surrounding the structure and incorporates time-dependent non-reflecting boundary conditions on the fluid truncation boundary. Energy estimates are obt ained which allow us to prove the unconditional stability of the metho d for the coupled fluid-structure problem with absorbing boundaries. T he methods developed are especially useful for the application of adap tive solution strategies for transient acoustics in which unstructured space-time meshes are used to track waves propagating along space-tim e characteristics. An important feature of the space-time formulation is the incorporation of temporal jump operators which allow for finite element interpolations that are discontinuous in time. For additional stability, least-squares operators based on local residuals of the st ructural acoustics equations including the non-reflecting boundary con ditions are incorporated. The energy decay estimates and high-order ac curacy predicted by our a priori error estimates are demonstrated nume rically in a simple canonical example.