In this paper, we analyze a divergence-free finite element method to solve a fluid–structure interaction spectral problem in the three-dimensional case. The unknowns of the resulting formulation are the fluid and solid displacements and the fluid pressure on the interface separating both media. The resulting mixed eigenvalue problem is approximated by using appropriate basis of the divergence-free lowest order Raviart–Thomas elements for the fluid, piecewise linear elements for the solid and piecewise constant elements for the interface pressure. It is proved that eigenvalues and eigenfunctions are correctly approximated and some numerical results are reported in order to assess the performance of the method.

Divergence-free finite elements for the numerical solution of a hydroelastic vibration problem / Alonso-Rodriguez, Ana; Camano, Jessika; De Los Santos, Eduardo; Rodriguez, Rodolfo. - In: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0749-159X. - STAMPA. - 2023, 39:1(2023), pp. 163-186. [10.1002/num.22862]

Divergence-free finite elements for the numerical solution of a hydroelastic vibration problem

Alonso-Rodriguez, Ana;De Los Santos, Eduardo;
2023-01-01

Abstract

In this paper, we analyze a divergence-free finite element method to solve a fluid–structure interaction spectral problem in the three-dimensional case. The unknowns of the resulting formulation are the fluid and solid displacements and the fluid pressure on the interface separating both media. The resulting mixed eigenvalue problem is approximated by using appropriate basis of the divergence-free lowest order Raviart–Thomas elements for the fluid, piecewise linear elements for the solid and piecewise constant elements for the interface pressure. It is proved that eigenvalues and eigenfunctions are correctly approximated and some numerical results are reported in order to assess the performance of the method.
2023
1
Alonso-Rodriguez, Ana; Camano, Jessika; De Los Santos, Eduardo; Rodriguez, Rodolfo
Divergence-free finite elements for the numerical solution of a hydroelastic vibration problem / Alonso-Rodriguez, Ana; Camano, Jessika; De Los Santos, Eduardo; Rodriguez, Rodolfo. - In: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0749-159X. - STAMPA. - 2023, 39:1(2023), pp. 163-186. [10.1002/num.22862]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/334144
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