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Nonconforming Methods for Nonlinear Elasticity Problems

  • Bernd Flemisch
  • Barbara I. Wohlmuth
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 55)

Abstract

Domain decomposition methods are studied for several problems exhibiting nonlinearities in terms of curved interfaces and/or underlying model equations. In order to retain as much flexibility as possible, we do not require the subdomain grids to match along their common interfaces. Dual Lagrange multipliers are employed to generate efficient and robust transmission operators between the subdomains. Various numerical examples are presented to illustrate the applicability of the approach.

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References

  1. 1.
    F. Ben Belgacem, The mortar finite element method with Lagrange multipliers, Numer. Math., 84 (1999), pp. 173–197.zbMATHCrossRefGoogle Scholar
  2. 2.
    C. Bernardi, Y. Maday, and A. T. Patera, A New Non Conforming Approach to Domain Decomposition: The Mortar Element Method, vol. 299 of Pitman Res. Notes Math. Ser., Pitman, 1994, pp. 13–51.Google Scholar
  3. 3.
    D. Braess and W. Dahmen, Stability estimates of the mortar finite element method for 3-dimensional problems, East-West J. Numer. Math., 6 (1998), pp. 249–264.zbMATHGoogle Scholar
  4. 4.
    B. Flemisch, J. M. Melenk, and B. I. Wohlmuth, Mortar methods with curved interfaces, Appl. Numer. Math., 54 (2005), pp. 339–361.zbMATHCrossRefGoogle Scholar
  5. 5.
    B. Flemisch, M. A. Puso, and B. I.Wohlmuth, A new dual mortar method for curved interfaces: 2D elasticity, Internat. J. Numer. Methods Engrg., 63 (2005), pp. 813–832.zbMATHCrossRefGoogle Scholar
  6. 6.
    W. J. Gordon and C. A. Hall, Transfinite element methods: blending-function interpolation over arbitrary curved element domains, Numer. Math., 21 (1973), pp. 109–129.zbMATHCrossRefGoogle Scholar
  7. 7.
    S. Hüeber, M. Mair, and B. I. Wohlmuth, A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems, Appl. Numer. Math., 54 (2005), pp. 555–576.zbMATHCrossRefGoogle Scholar
  8. 8.
    C. Kim, R. Lazarov, J. Pasciak, and P. Vassilevski, Multiplier spaces for the mortar finite element method in three dimensions, SIAM J. Numer. Anal., 39 (2001), pp. 519–538.zbMATHCrossRefGoogle Scholar
  9. 9.
    M. A. Puso, A 3D mortar method for solid mechanics, Internat. J. Numer. Methods Engrg., 59 (2004), pp. 315–336.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Bernd Flemisch
    • 1
  • Barbara I. Wohlmuth
    • 1
  1. 1.Institute for Applied Analysis and Numerical SimulationUniversity of StuttgartStuttgartGermany

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