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

• Autorzy: Costa R. , Machado G. J. , Clain S.

Identyfikatory

DOI

10.1515/amcs-2015-0039

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2015
• Tom: Vol. 25, no. 3
• Strony: 529--537
• Opis fizyczny: Bibliogr. 16 poz., rys., tab.

Twórcy

autor

Costa R.

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

autor

Machado G. J.

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

autor

Clain S.

• 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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