On Conforming Tetrahedralisations of Prismatic Partitions

  • Sergey KorotovEmail author
  • Michal Křížek
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 47)


We present an algorithm for conform (face-to-face) subdividing prismatic partitions into tetrahedra. This algorithm can be used in the finite element calculations and analysis.


Finite element method Prismatic element Tetrahedral mesh Linear elements 

Mathematical Subject Classification

65N50 51M20 



This work was supported by Grant MTM2011-24766 of the MICINN, Spain, and the Grant no. IAA 100190803 of the Grant Agency of the Academy of Sciences of the Czech Republic. The authors are indebted to A. and Z. Horváth for fruitful discussions.


  1. 1.
    Apel, T., Düvelmeyer, N.: Transformation of hexahedral finite element meshes into tetrahedral meshes according to quality criteria. Preprint SFB393/03-09. Tech. Univ. Chemnitz, pp. 1–12 (2003)Google Scholar
  2. 2.
    Ciarlet, P.G.: Basic error estimates for elliptic problems. In: Ciarlet, P., Lions, G.J.L. (eds.) Handbook of Numerical Analysis, vol. II. North-Holland, Amsterdam (1991)Google Scholar
  3. 3.
    Hannukainen, A., Korotov, S., Vejchodský, T.: Discrete maximum principle for FE solutions of the diffusion-reaction problem on prismatic meshes. J. Comput. Appl. Math. 226, 275–287 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Karátson, J., Korotov, S., Křížek, M.: On discrete maximum principles for nonlinear elliptic problems. Math. Comp. Simulation 76, 99–108 (2007)CrossRefzbMATHGoogle Scholar
  5. 5.
    Korotov, S., Vejchodský, T.: A comparison of simplicial and block finite elements. In: Kreiss, G., et al. (eds.) Proceedings Eighth European Conference on Numerical Mathematics and Advanced Applications (ENUMATH2009), Uppsala, Sweden, pp. 531–540. Springer, Heidelberg (2010)Google Scholar
  6. 6.
    Křížek, M.: An equilibrium finite element method in three-dimensional elasticity. Apl. Mat. 27, 46–75 (1982) See also Google Scholar
  7. 7.
    Křížek, M., Lin, Q.: On diagonal dominance of stiffness matrices in 3D. East-West J. Numer. Math. 3, 59–69 (1995)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Křížek, M., Neittaanmäki, P.: Finite element approximation of variational problems and applications. In: Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 50, Longman Scientific & Technical, Harlow (1990)Google Scholar
  9. 9.
    Liu, L., Davies, K.B., Yuan, K., Křížek, M.: On symmetric pyramidal finite elements. Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 11, 213–227 (2004)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Nečas, J., Hlaváček, I.: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Elsevier, Amsterdam (1981)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.BCAM – Basque Center for Applied MathematicsAlameda de Mazarredo 14Basque CountrySpain
  2. 2.IKERBASQUEBasque Foundation for ScienceBilbaoSpain
  3. 3.Institute of MathematicsAcademy of SciencesPrague 1Czech Republic

Personalised recommendations