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

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...

Full description

Saved in:
Bibliographic Details
Published in:Numerical methods for partial differential equations 2023-01, Vol.39 (1), p.163-186
Main Authors: Alonso‐Rodríguez, Ana, Camaño, Jessika, De Los Santos, Eduardo, Rodríguez, Rodolfo
Format: Article
Language:English
Subjects:
Approximation
Divergence
Eigenvalues
Eigenvectors
Finite element method
finite elements
Fluid pressure
Fluid-structure interaction
spectral problems
Vibration analysis
vibrations
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0749-159X
1098-2426
DOI:10.1002/num.22862