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...
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| Veröffentlicht in: | Numerical methods for partial differential equations 2023-01, Vol.39 (1), p.163-186 |
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| creator | Alonso‐Rodríguez, Ana Camaño, Jessika De Los Santos, Eduardo Rodríguez, Rodolfo |
| description | 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. |
| doi_str_mv | 10.1002/num.22862 |
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| subjects | Approximation Divergence Eigenvalues Eigenvectors Finite element method finite elements Fluid pressure Fluid-structure interaction spectral problems Vibration analysis vibrations |
| title | Divergence‐free finite elements for the numerical solution of a hydroelastic vibration problem |
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