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Finite element methods for the Helmholtz equation in an exterior domain: Model problems. (English) Zbl 0760.76047
Summary: Finite element methods are presented for the reduced wave equation is unbounded domains. Model problems of radiation with inhomogeneous Neumann boundary conditions, including the effects of a moving acoustic medium, are examined for the entire range of propagation and decay. Exterior boundary conditions for the computational problem over a finite domain are derived from an exact relation between the solution and its derivatives on that boundary. Galerkin, Galerkin/least-squares and Galerkin/gradient least-squares finite element methods are evaluated by comparing errors pointwise and in integral norms. The Galerkin/least- squares method is shown to exhibit superior behavior for this class of problems.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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