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

Ricardo Costa; Gaspar J. Machado; Stéphane Clain

International Journal of Applied Mathematics and Computer Science (2015)

- Volume: 25, Issue: 3, page 529-537
- ISSN: 1641-876X

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topRicardo Costa, Gaspar J. Machado, and Stéphane Clain. "A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation." International Journal of Applied Mathematics and Computer Science 25.3 (2015): 529-537. <http://eudml.org/doc/271772>.

@article{RicardoCosta2015,

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.},

author = {Ricardo Costa, Gaspar J. Machado, Stéphane Clain},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {finite volume method; polynomial reconstruction operator; harmonic operator; biharmonic operator; high-order method},

language = {eng},

number = {3},

pages = {529-537},

title = {A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation},

url = {http://eudml.org/doc/271772},

volume = {25},

year = {2015},

}

TY - JOUR

AU - Ricardo Costa

AU - Gaspar J. Machado

AU - Stéphane Clain

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

JO - International Journal of Applied Mathematics and Computer Science

PY - 2015

VL - 25

IS - 3

SP - 529

EP - 537

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/271772

ER -

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