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Paper details
Number 3 - September 2015
Volume 25 - 2015
A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation
Ricardo Costa, Gaspar J. Machado, Stéphane Clain
Abstract
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.
Keywords
finite volume method, polynomial reconstruction operator, harmonic operator, biharmonic operator, high-order method