Finite element analysis for a Herrmann pressure formulation of the elastoacoustic problem with variable coefficients
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917059974135808 |
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| author | Khan, Arbaz Lepe, Felipe Mora, David Ruíz-Baier, Ricardo Vellojin, Jesus |
| author_facet | Khan, Arbaz Lepe, Felipe Mora, David Ruíz-Baier, Ricardo Vellojin, Jesus |
| contents | In two and three dimensions, this study is focused on the numerical analysis of an eigenproblem associated with a fluid-structure model for sloshing and elasto-acoustic vibration. We use a displacement-Herrmann pressure formulation for the solid, while for the fluid, a pure displacement formulation is considered. Under this approach we propose a non conforming locking-free method based on classic finite elements to approximate the natural frequencies (of the eigenmodes) of the coupled system. Employing the theory for non-compact operators we prove convergence and error estimates. Also we propose an a posteriori error estimator for this coupled problem which is shown to be efficient and reliable. All the presented theory is contrasted with a set of numerical tests in 2D and 3D. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02782 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite element analysis for a Herrmann pressure formulation of the elastoacoustic problem with variable coefficients Khan, Arbaz Lepe, Felipe Mora, David Ruíz-Baier, Ricardo Vellojin, Jesus Numerical Analysis 65N30, 65N12, 76D07, 65N15 In two and three dimensions, this study is focused on the numerical analysis of an eigenproblem associated with a fluid-structure model for sloshing and elasto-acoustic vibration. We use a displacement-Herrmann pressure formulation for the solid, while for the fluid, a pure displacement formulation is considered. Under this approach we propose a non conforming locking-free method based on classic finite elements to approximate the natural frequencies (of the eigenmodes) of the coupled system. Employing the theory for non-compact operators we prove convergence and error estimates. Also we propose an a posteriori error estimator for this coupled problem which is shown to be efficient and reliable. All the presented theory is contrasted with a set of numerical tests in 2D and 3D. |
| title | Finite element analysis for a Herrmann pressure formulation of the elastoacoustic problem with variable coefficients |
| topic | Numerical Analysis 65N30, 65N12, 76D07, 65N15 |
| url | https://arxiv.org/abs/2511.02782 |