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TitleA sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation
Author(s)Costa, Ricardo Daniel Pereira
Machado, Gaspar J.
Clain, Stéphane
KeywordsFinite volume method
Polynomial reconstruction operator
Harmonic operator
Biharmonic operator
High-order method
Issue date2015
PublisherWalter de Gruyter GmbH
JournalInternational Journal of Applied Mathematics and Computer Science
Abstract(s)A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one- dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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