BIT Numerical Mathematics

, Volume 37, Issue 3, pp 720–738 | Cite as

Two different approaches for matching nonconforming grids: The Mortar Element method and the Feti Method

  • C. Lacour
  • Y. Maday


When using domain decomposition in a finite element framework for the approximation of second order elliptic or parabolic type problems, it has become appealing to tune the mesh of each subdomain to the local behaviour of the solution. The resulting discretization being then nonconforming, different approaches have been advocated to match the admissible discrete functions. We recall here the basics of two of them, the Mortar Element method and the Finite Element Tearing and Interconnecting (FETI) method, and aim at comparing them. The conclusion, both from the theoretical and numerical point of view, is in favor of the mortar element method.

AMS subject classification

65F30 65M60 65Y05 

Key words

Domain decomposition mortar finite element method nonmatching grids saddle-point problem hybrid methods 


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  1. 1.
    G. S. Abdoulaev, Y. Achdou, Yu. A. Kuznetsov, and O. Pironneau,The numerical implementation of the domain decomposition method with mortar finite elements for a 3D problem, preprint.Google Scholar
  2. 2.
    A. Agouzal and J. M. Thomas,Une méthode d'éléments finis hybrides en décomposition de domaines, M2 AN, 29:6 (1996), pp. 749–764.MathSciNetGoogle Scholar
  3. 3.
    Y. Achdou and Y. Maday, review article in preparation.Google Scholar
  4. 4.
    F. Ben Belgacem,The mortar finite element method with Lagrange multipliers, Rapport interne MIP numero 94-1, Université Paul Sabatier, 1994.Google Scholar
  5. 5.
    F. Ben Belgacem and Y. Maday,Coupling spectral and finite element discretizations for second order elliptic three dimensional equations, preprint.Google Scholar
  6. 6.
    C. Bernardi, Y. Maday, and A. T. Patera,A new nonconforming approach to domain decomposition: the mortar element method, in Collège de France Seminar, H. Brezis, and J.-L. Lions, eds., Pitman, 1990.Google Scholar
  7. 7.
    F. Brezzi and D. Marini,A three fields domain decomposition method, in Contemporary Mathematics A. Quarteroni, J. Periaux, Y. A. Kuznetsov, and O. B. Widlund, eds., Vol. 157, 1994, pp. 27–34.Google Scholar
  8. 8.
    L. Cazabeau,Méthodes multi-domaines pour la résolution des équations de Navier-Stokes en simulation numérique directe, PhD. thesis in preparation.Google Scholar
  9. 9.
    C. Farhat and M. Geradin,Using a reduced number of Lagrange multipliers for assembling parallel incomplete field finite element approximations, Comput. Methods Appl. Mech. Engrg., 97 (1992), pp. 333–354.MATHCrossRefGoogle Scholar
  10. 10.
    C. Farhat and F. X. Roux,A method of finite element tearing and interconnecting and its parallel solution algorithm, Internat. J. Numer. Meth. Engrg., 32 (1991), pp. 1205–1227.MATHCrossRefGoogle Scholar
  11. 11.
    D. E. Keyes and J. Xu,Domain decomposition methods in scientific and engineering computing, in Proceedings of the Seventh International Conference on Domain Decomposition, The Pennsylvania State University, October 27–30, 1993. Contemporary Mathematics, Vol 180, 1994.Google Scholar
  12. 12.
    C. Lacour,Iterative substructuring preconditioners for the mortar finite element method, in Proceedings of the Ninth International Conference on Domain Decomposition, Bergen, 1996, John Wiley & Sons, to appear.Google Scholar
  13. 13.
    P. Le Tallec, T. Sassi, and M. Vidrascu,Three-dimensional domain decomposition methods with nonmatching grids and unstructured coarse solvers, in Proceedings of the Seventh International Conference on Domain Decomposition, The Pennsylvania State University, October 27–30, 1993. Contemporary Mathematics, Vol. 180, 1994, pp. 61–74.Google Scholar
  14. 14.
    Y. Maday, D. Meiron, A. T. Patera and E. M. Rønquist,Analysis of iterative methods for the steady and unsteady Stokes problem: Application to spectral element discretizations, SIAM J. Sci. Comput., 14:2 (1993), pp. 310–337.MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Proceedings of the Eighth and Ninth International Conference on Domain Decomposition, John Wiley & Sons, to appear.Google Scholar
  16. 16.
    P. A. Raviart and J. M. Thomas,Primal hybrid finite element methods for second order elliptic equations, Math. Comp., 31 (1977), pp. 391–413.MATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    F. X. Roux,Méthode de décomposition de domaine à l'aide de multiplicateurs de Lagrange et application à la résolution en parallèle des équations de l'élasticité linéaire, Ph. D. thesis, 1989, Universite Pierre et Marie Curie, Paris.Google Scholar
  18. 18.
    J. M. Thomas,Formulation mixte des équations aux dérivées partielles du second ordre elliptiques, Ph.D. thesis, 1977, University Paris VI.Google Scholar
  19. 19.
    H. Yserentant,On the multi-level splitting of finite element spaces, Numer. Math., 49 (1986), pp. 379–412.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© BIT Foundation 1997

Authors and Affiliations

  • C. Lacour
    • 1
  • Y. Maday
    • 1
    • 2
  1. 1.ONERAChatillon CedexFrance
  2. 2.ASCIUniversité Paris SudOrsay CedexFrance

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