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1 International Journal of Applied Mathematics and Computer Science

1 2015

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

Costa R., Machado G. J., Clain S.

International Journal of Applied Mathematics and Computer Science

2015

Vol. 25, no. 3

529--537

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.