Finite element analysis for a Herrmann pressure formulation of the elastoacoustic problem with variable coefficients

Fuente: arXiv
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Main Authors: Khan, Arbaz, Lepe, Felipe, Mora, David, Ruíz-Baier, Ricardo, Vellojin, Jesus
Format: Preprint
Published: 2025
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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