Abstract
The problem of elastic-fluid scattering is studied by combined integral equations for the exterior acoustic fluid and finite element methods for the elastic structure. These yield reduced problems over finite domains. The well-known difficulty with exterior integral equation methods at critical frequencies carries over to the reduced problem. A procedure is given to overcome this difficulty and a complete analysis of this procedure is provided, showing existence, uniqueness, and optimal convergence for the coupled problems. This method is termed stable. Numerical experiments confirm that the new approach is valid for all frequencies and indicate that variational methods are preferable to collocation in the treatment of integral equations, even for purely exterior problems. Our method is fully variational and may be expressed in a symmetric form.
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