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Divergence-free finite elements for the numerical solution of a hydroelastic vibration problem |
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| Authors: | Ana Alonso-Rodríguez Jessika Camaño Eduardo De Los Santos Rodolfo Rodríguez |
| Institution: | 1. Department of Mathematics, University of Trento, Trento, Italy;2. Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Concepción, Chile;3. CI2MA, Universidad de Concepción, Concepción, Chile
Scientific and Applied Computing Laboratory, Polytechnic School, National University of Asuncion, San Lorenzo, Paraguay;4. CI2MA, Universidad de Concepción, Concepción, Chile Departamento de Ingeniería Matemática, Universidad de Concepción, Concepción, Chile |
| 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. |
| Keywords: | finite elements spectral problems vibrations |