<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></abstract>

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.

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

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

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

Published Online: Sep 30, 2015

Page range: 529 - 537

Received: Oct 21, 2013

DOI: https://doi.org/10.1515/amcs-2015-0039

© by Gaspar J. Machado

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.