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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Analysis of a finite element method for pressure/potential formulation of elastoacoustic spectral problems
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by Alfredo Bermúdez and Rodolfo Rodríguez PDF
Math. Comp. 71 (2002), 537-552 Request permission

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
  • Email: mabermud@usc.es
  • Rodolfo Rodríguez
  • Affiliation: Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
  • Email: rodolfo@ing-mat.udec.cl
  • 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)
  • © Copyright 2001 American Mathematical Society
  • Journal: Math. Comp. 71 (2002), 537-552
  • MSC (2000): Primary 65N25, 65N30; Secondary 70J30, 74F10, 76Q05
  • DOI: https://doi.org/10.1090/S0025-5718-01-01335-7
  • MathSciNet review: 1885614