An $hp$ Finite Element Method to Solve a Fluid-Solid Vibration Problem

This paper deals with a two-dimensional fluid-solid vibration problem arising from nuclear engineering: the vibration of elastically mounted tubes immersed in a cavity filled with fluid. A convenient variational formulation of this problem, valid for compressible and incompressible fluids, is introd...

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Vydáno v:SIAM journal on scientific computing Ročník 34; číslo 5; s. A2533 - A2557
Hlavní autoři: Padra, Claudio, Rodríguez, Rodolfo, Scheble, Mario
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.01.2012
Témata:
Approximation
Eigenvalues
Finite element analysis
Nuclear engineering
Velocity
ISSN:1064-8275, 1095-7197
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Abstract This paper deals with a two-dimensional fluid-solid vibration problem arising from nuclear engineering: the vibration of elastically mounted tubes immersed in a cavity filled with fluid. A convenient variational formulation of this problem, valid for compressible and incompressible fluids, is introduced. An $hp$ finite element method is used for its discretization, which leads to a well posed matrix eigenvalue problem. Optimal order a priori error estimates are proved for eigenfunctions and eigenvalues. Then, local a posteriori error indicators are defined and its efficiency and reliability are studied. An adaptive scheme driven by these indicators is proposed and numerically tested. [PUBLICATION ABSTRACT]
AbstractList This paper deals with a two-dimensional fluid-solid vibration problem arising from nuclear engineering: the vibration of elastically mounted tubes immersed in a cavity filled with fluid. A convenient variational formulation of this problem, valid for compressible and incompressible fluids, is introduced. An $hp$ finite element method is used for its discretization, which leads to a well posed matrix eigenvalue problem. Optimal order a priori error estimates are proved for eigenfunctions and eigenvalues. Then, local a posteriori error indicators are defined and its efficiency and reliability are studied. An adaptive scheme driven by these indicators is proposed and numerically tested. [PUBLICATION ABSTRACT]
Author Padra, Claudio
Scheble, Mario
Rodríguez, Rodolfo
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CitedBy_id crossref_primary_10_1016_j_apnum_2015_12_001
crossref_primary_10_1016_j_camwa_2025_02_010
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Cites_doi 10.1016/j.cma.2010.08.003
10.1023/A:1014268310921
10.1016/0045-7825(83)90052-X
10.1137/1036141
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SubjectTerms Approximation
Eigenvalues
Finite element analysis
Nuclear engineering
Velocity
Title An $hp$ Finite Element Method to Solve a Fluid-Solid Vibration Problem
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