Mathematics of Computation

Author(s): Alfredo Bermúdez; Ricardo Durán; Rodolfo Rodríguez.
Journal: Math. Comp. 67 (1998), 111-136.
MSC (1991): Primary 65N25, 65N30; Secondary 70J30, 73K70, 76Q05
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Abstract: This paper deals with a finite element method to solve interior fluid-structure vibration problems valid for compressible and incompressible fluids. It is based on a displacement formulation for both the fluid and the solid. The pressure of the fluid is also used as a variable for the theoretical analysis yielding a well posed mixed linear eigenvalue problem. Lowest order triangular Raviart-Thomas elements are used for the fluid and classical piecewise linear elements for the solid. Transmission conditions at the fluid-solid interface are taken into account in a weak sense yielding a nonconforming discretization. The method does not present spurious or circulation modes for nonzero frequencies. Convergence is proved and error estimates independent of the acoustic speed are given. For incompressible fluids, a convenient equivalent stream function formulation and a post-process to compute the pressure are introduced.

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Alfredo Bermúdez
Affiliation: Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain
Email: bermudez@zmat.usc.es

Ricardo Durán
Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 -- Buenos Aires, Argentina
Email: rduran@mate.dm.uba.ar

Alfredo Berm�dez and Rodolfo Rodr�guez,Numerical computation of elastoacoustic vibrations with interface damping,�quations aux d�riv�es partielles et applications. [Partial differential equations and applications] Articles d�di�s � Jacques-Louis Lions. [Articles dedicated to Jacques-Louis Lions] (Paris, May 26, 1998), Gauthier-Villars, �ditions Scientifiques et M�dicales Elsevier, Paris,France, 1998, pp. 165-187. (English) MR CMP 1 648 211 (99:03) 00B30 (35-06)

A. Bermudez, R. Duran, R. Rodriguez, Finite element solution of incompressible fluid-structure vibration problems, International Journal for Numerical Methods in Engineering 40 (1997), 1435-1448.

A. Bermudez, R. Rodriguez, Finite element analysis of sloshing and hydroelastic vibrations under gravity, M2AN Mathematical Modelling and Numerical Analysis 33 (1999), 305-327.

A. Alonso, A. Dello Russo, V. Vampa, A posteriori error estimates in finite element acoustic analysis, Journal of Computational and Applied Mathematics 117 (2000), 105-119.

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