Have a personal or library account? Click to login
A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation Cover

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

Open Access
|Sep 2015

References

  1. Audusse, E. and Bristeau, M.-O. (2007). Finite-volume solvers for a multilayer Saint-Venant system, International Journal of Applied Mathematics and Computer Science 17(3): 311-320, DOI: 10.2478/v10006-007-0025-0.10.2478/v10006-007-0025-0
  2. Barreira, L., Teixeira, C. and Fonseca, E. (2008). Avaliação da resistência do colo do fémur utilizando o modelo de elementos finitos, Revista da Associação Portuguesa de Análise Experimental de Tensões 16: 19-24.
  3. Branco, C.M. (2011). Mecânica dos Materiais, Fundação Calouste Gulbenkian, Lisboa.
  4. Clain, S., Diot, S. and Loubère, R. (2011). A high-order polynomial finite volume method for hyperbolic system of conservation laws with multi-dimensional optimal order detection (MOOD), Journal of Computational Physics 230(10): 4028-4050.10.1016/j.jcp.2011.02.026
  5. Clain, S., Machado, G.J., Nóbrega, J.M. and Pereira, R.M.S. (2013). A sixth-order finite volume method for the convection-diffusion problem with discontinuous coefficients, Computer Methods in Applied Mechanics and Engineering 267(1): 43-64.10.1016/j.cma.2013.08.003
  6. Diot, S., Clain, S. and Loubère, R. (2011). Multi-dimensional optimal order detection (mood)-a very high-order finite volume scheme for conservation laws on unstructured meshes, 6th Finite Volume and Complex Application, Prague, Czech Republic, pp. 263-271.
  7. Dumbser, M. and Munz, C.-D. (2007). On source terms and boundary conditions using arbitrary high order discontinuous Galerkin schemes, International Journal of Applied Mathematics and Computer Science 17(3): 297-310, DOI: 10.2478/v10006-007-0024-1.10.2478/v10006-007-0024-1
  8. Eymard, R., Gallouët, T. and Herbin, R. (2000). The finite volume method, in P. Ciarlet and J.L. Lions (Eds.), Handbook for Numerical Analysis, North Holland, Amsterdam, pp. 715-1022.
  9. Hern´andez, J. (2002). High-order finite volume schemes for the advection-diffusion equation, International Journal for Numerical Methods in Engineering 53(5): 1211-1234.10.1002/nme.335
  10. Kroner, D. (1997). Numerical Schemes for Conservation Laws, Wiley-Teubneur Publishers, Chichester.
  11. Leveque, R.J. (2002). Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge.10.1017/CBO9780511791253
  12. Ollivier-Gooch, C. and Altena, M.V. (2002). A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation, Journal of Computational Physics 181(2): 729-752.10.1006/jcph.2002.7159
  13. Ramos, A. and Simoes, J.A. (2009). Caracterização de cavilhas de fixação intra-medular de estabilização de fracturas ósseas, Revista da Associação Portuguesa de Análise Experimental de Tensões 17: 49-55.
  14. Toro, E. (2009). Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, Berlin/Heidelberg.10.1007/b79761
  15. Toro, E. and Hidalgo, A. (2009). Ader finite volume schemes for nonlinear reaction-diffusion equations, Applied Numerical Mathematics 59(1): 73-100.10.1016/j.apnum.2007.12.001
  16. Trangenstein, J.A. (2009). Numerical Solution of Hyperbolic Partial Differential Equations, Cambridge University Press, Cambridge. 10.1017/CBO9781139025508
DOI: https://doi.org/10.1515/amcs-2015-0039 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 529 - 537
Submitted on: Oct 21, 2013
Published on: Sep 30, 2015
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2015 Ricardo Costa, Gaspar J. Machado, Stéphane Clain, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.