A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation

• Autorzy: Ricardo Costa , Gaspar J. Machado , Stéphane Clain
• Języki publikacji: EN

Abstrakty

EN

A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional 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.

Słowa kluczowe

EN

finite volume method; polynomial reconstruction operator; harmonic operator; biharmonic operator; high-order method

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2015
• Tom: 25
• Numer: 3
• Strony: 529-537

Daty

wydano

2015

otrzymano

2013-10-21

poprawiono

2014-07-31

Twórcy

autor

Ricardo Costa

• Centre of Mathematics, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal

autor

Gaspar J. Machado

• Centre of Mathematics, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal

autor

Stéphane Clain

• Centre of Mathematics, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
• Institute of Mathematics, Paul Sabatier University, 118, route de Narbonne, 31062 Toulouse, France

Bibliografia

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Identyfikatory

DOI

10.1515/amcs-2015-0039