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...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Armentano, Maria Gabriela, Padra, Claudio
Publicado: 2011
Materias:
A posteriori error estimates
Finite elements
Fluid-structure interaction
Hp Version
Spectral approximation
Vibration problem
Finite Element
Hp-version
Posteriori error estimates
Spectral approximations
Adaptive algorithms
Eigenvalues and eigenfunctions
Finite element method
Fluid structure interaction
Fluids
Vibration analysis
Convergence of numerical methods
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00457825_v200_n1-4_p178_Armentano
http://hdl.handle.net/20.500.12110/paper_00457825_v200_n1-4_p178_Armentano
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00457825_v200_n1-4_p178_Armentano
record_format dspace
spelling paper:paper_00457825_v200_n1-4_p178_Armentano2023-06-08T15:05:20Z An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations Armentano, Maria Gabriela Padra, Claudio 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. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00457825_v200_n1-4_p178_Armentano 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, Maria Gabriela
Padra, Claudio
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.
author Armentano, Maria Gabriela
Padra, Claudio
author_facet Armentano, Maria Gabriela
Padra, Claudio
author_sort Armentano, Maria Gabriela
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
publishDate 2011
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00457825_v200_n1-4_p178_Armentano
http://hdl.handle.net/20.500.12110/paper_00457825_v200_n1-4_p178_Armentano
work_keys_str_mv AT armentanomariagabriela anhpfiniteelementadaptiveschemetosolvethelaplacemodelforfluidsolidvibrations
AT padraclaudio anhpfiniteelementadaptiveschemetosolvethelaplacemodelforfluidsolidvibrations
AT armentanomariagabriela hpfiniteelementadaptiveschemetosolvethelaplacemodelforfluidsolidvibrations
AT padraclaudio hpfiniteelementadaptiveschemetosolvethelaplacemodelforfluidsolidvibrations
_version_ 1768545871247441920

Ejemplares similares