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Analysis of a finite element method for pressure/potential formulation of elastoacoustic spectral problems

Authors: Alfredo Bermúdez and Rodolfo Rodríguez
Journal: Math. Comp. 71 (2002), 537-552
MSC (2000): Primary 65N25, 65N30; Secondary 70J30, 74F10, 76Q05
Published electronically: September 17, 2001
MathSciNet review: 1885614
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Abstract: A finite element method to approximate the vibration modes of a structure enclosing an acoustic fluid is analyzed. The fluid is described by using simultaneously pressure and displacement potential variables, whereas displacement variables are used for the solid. A mathematical analysis of the continuous spectral problem is given. The problem is discretized on a simplicial mesh by using piecewise constant elements for the pressure and continuous piecewise linear finite elements for the other fields. Error estimates are settled for approximate eigenvalues and eigenfrequencies. Finally, implementation issues are discussed.

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Additional Information

Alfredo Bermúdez
Affiliation: Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain

Rodolfo Rodríguez
Affiliation: Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

Keywords: Finite element spectral approximation, elastoacoustic vibrations
Received by editor(s): April 13, 1999
Received by editor(s) in revised form: August 14, 2000
Published electronically: September 17, 2001
Additional Notes: The first author was supported by DGESIC project PB97-0508 (Spain)
The second author was supported by FONDECYT No. 1.990.346 and FONDAP in Applied Mathematics (Chile)
Article copyright: © Copyright 2001 American Mathematical Society

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