Acoustic vibration problem for dissipative fluids
Provides a rigorous numerical analysis for a specific class of eigenvalue problems in computational acoustics.
The paper analyzes a finite element method for a quadratic eigenvalue problem from acoustic vibrations in dissipative fluids, proving it is free of spurious modes and converges with optimal order.
In this paper we analyze a finite element method for solving a quadratic eigenvalue problem derived from the acoustic vibration problem for a heterogeneous dissipative fluid. The problem is shown to be equivalent to the spectral problem for a noncompact operator and athorough spectral characterization is given. The numerical discretization of the problem is based on Raviart-Thomas finite elements. The method is proved to be free of spurious modes and to converge with optimal order. Finally, we report numerical tests which allow us to assess the performance of the method.