An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations
In this paper we introduce an hp finite element method to solve a two-dimensional fluid-structure spectral problem. This problem arises from the computation of the vibration modes of a bundle of parallel tubes immersed in an incompressible fluid. We prove the convergence of the method and a priori e...
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todo:paper_00457825_v200_n1-4_p178_Armentano2023-10-03T14:52:03Z An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations Armentano, M.G. Padra, C. Rodríguez, R. Scheble, M. A posteriori error estimates Finite elements Fluid-structure interaction Hp Version Spectral approximation Vibration problem Finite Element Hp-version Posteriori error estimates Spectral approximations Vibration problem Adaptive algorithms Eigenvalues and eigenfunctions Finite element method Fluid structure interaction Fluids Vibration analysis Convergence of numerical methods In this paper we introduce an hp finite element method to solve a two-dimensional fluid-structure spectral problem. This problem arises from the computation of the vibration modes of a bundle of parallel tubes immersed in an incompressible fluid. We prove the convergence of the method and a priori error estimates for the eigenfunctions and the eigenvalues. We define an a posteriori error estimator of the residual type which can be computed locally from the approximate eigenpair. We show its reliability and efficiency by proving that the estimator is equivalent to the energy norm of the error up to higher order terms, the equivalence constant of the efficiency estimate being suboptimal in that it depends on the polynomial degree. We present an hp adaptive algorithm and several numerical tests which show the performance of the scheme, including some numerical evidence of exponential convergence. © 2010 Elsevier B.V. Fil:Armentano, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Padra, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00457825_v200_n1-4_p178_Armentano |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
A posteriori error estimates Finite elements Fluid-structure interaction Hp Version Spectral approximation Vibration problem Finite Element Hp-version Posteriori error estimates Spectral approximations Vibration problem Adaptive algorithms Eigenvalues and eigenfunctions Finite element method Fluid structure interaction Fluids Vibration analysis Convergence of numerical methods |
spellingShingle |
A posteriori error estimates Finite elements Fluid-structure interaction Hp Version Spectral approximation Vibration problem Finite Element Hp-version Posteriori error estimates Spectral approximations Vibration problem Adaptive algorithms Eigenvalues and eigenfunctions Finite element method Fluid structure interaction Fluids Vibration analysis Convergence of numerical methods Armentano, M.G. Padra, C. Rodríguez, R. Scheble, M. An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations |
topic_facet |
A posteriori error estimates Finite elements Fluid-structure interaction Hp Version Spectral approximation Vibration problem Finite Element Hp-version Posteriori error estimates Spectral approximations Vibration problem Adaptive algorithms Eigenvalues and eigenfunctions Finite element method Fluid structure interaction Fluids Vibration analysis Convergence of numerical methods |
description |
In this paper we introduce an hp finite element method to solve a two-dimensional fluid-structure spectral problem. This problem arises from the computation of the vibration modes of a bundle of parallel tubes immersed in an incompressible fluid. We prove the convergence of the method and a priori error estimates for the eigenfunctions and the eigenvalues. We define an a posteriori error estimator of the residual type which can be computed locally from the approximate eigenpair. We show its reliability and efficiency by proving that the estimator is equivalent to the energy norm of the error up to higher order terms, the equivalence constant of the efficiency estimate being suboptimal in that it depends on the polynomial degree. We present an hp adaptive algorithm and several numerical tests which show the performance of the scheme, including some numerical evidence of exponential convergence. © 2010 Elsevier B.V. |
format |
JOUR |
author |
Armentano, M.G. Padra, C. Rodríguez, R. Scheble, M. |
author_facet |
Armentano, M.G. Padra, C. Rodríguez, R. Scheble, M. |
author_sort |
Armentano, M.G. |
title |
An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations |
title_short |
An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations |
title_full |
An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations |
title_fullStr |
An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations |
title_full_unstemmed |
An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations |
title_sort |
hp finite element adaptive scheme to solve the laplace model for fluid-solid vibrations |
url |
http://hdl.handle.net/20.500.12110/paper_00457825_v200_n1-4_p178_Armentano |
work_keys_str_mv |
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