A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation - Costa, Ricardo; Machado, Gaspar J.; Clain, Stéphane (Zielona Góra: Uniwersytet Zielonogórski)
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.
Keywords: finite volume method; polynomial reconstruction operator; harmonic operator; biharmonic operator; high-order method