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Abstract:

A quadratic eigenvalue problem arising in the determination of the vibration modes of an acoustic fluid contained in a cavity with absorbing walls is considered. The problem is shown to be equivalent to the spectral problem for a noncompact operator and a thorough spectral characterization is given. A numerical discretization based on Raviart-Thomas finite elements is analyzed. The method is proved to be free of spurious modes and to converge with optimal order. Implementation issues and numerical experiments confirming the theoretical results are reported.

Registro:

Documento: Artículo
Título:Finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics
Autor:Bermúdez, A.; Durán, R.G.; Rodríguez, R.; Solomin, J.
Filiación:Depto. de Matemática Aplicada, Univ. de Santiago de Compostela, 15706, Santiago de Compostela, Spain
Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina
Depto. de Ing. Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 172, 1900 - La Plata, Argentina
Palabras clave:Dissipative acoustics; Finite element spectral approximation; Quadratic eigenvalue problems
Año:2001
Volumen:38
Número:1
Página de inicio:267
Página de fin:291
DOI: http://dx.doi.org/10.1137/S0036142999360160
Título revista:SIAM Journal on Numerical Analysis
Título revista abreviado:SIAM J Numer Anal
ISSN:00361429
CODEN:SJNAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v38_n1_p267_Bermudez

Referencias:

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Citas:

---------- APA ----------
Bermúdez, A., Durán, R.G., Rodríguez, R. & Solomin, J. (2001) . Finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics. SIAM Journal on Numerical Analysis, 38(1), 267-291.
http://dx.doi.org/10.1137/S0036142999360160
---------- CHICAGO ----------
Bermúdez, A., Durán, R.G., Rodríguez, R., Solomin, J. "Finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics" . SIAM Journal on Numerical Analysis 38, no. 1 (2001) : 267-291.
http://dx.doi.org/10.1137/S0036142999360160
---------- MLA ----------
Bermúdez, A., Durán, R.G., Rodríguez, R., Solomin, J. "Finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics" . SIAM Journal on Numerical Analysis, vol. 38, no. 1, 2001, pp. 267-291.
http://dx.doi.org/10.1137/S0036142999360160
---------- VANCOUVER ----------
Bermúdez, A., Durán, R.G., Rodríguez, R., Solomin, J. Finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics. SIAM J Numer Anal. 2001;38(1):267-291.
http://dx.doi.org/10.1137/S0036142999360160