Acoustic vibration problem for dissipative fluids

Lepe, Felipe; Meddahi, Salim; Mora, David; Rodríguez, Rodolfo

doi:10.1090/mcom/3336

Acoustic vibration problem for dissipative fluids
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by Felipe Lepe, Salim Meddahi, David Mora and Rodolfo Rodríguez HTML | PDF

Math. Comp. 88 (2019), 45-71 Request permission

Abstract:

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 non-compact operator and a thorough 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.

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