Advertisement

Nonconforming Discretization Techniques for Overlapping Domain Decompositions

  • Bernd Flemisch
  • Michael Mair
  • Barbara Wohlmuth

Summary

For the numerical solution of coupled problems on two nested domains, two meshes are used which are completely independent to each other. Especially in the case of a moving subdomain, this leads to a great flexibility for employing different meshsizes, discretizations or model equations on the two domains. We present a general setting for these problems in terms of saddle point formulations, and investigate one- and bi-directionally coupled applications.

Keywords

Unique Solvability Saddle Point Problem Nest Domain Global Domain Continuous Bilinear Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Babuška, I. (1973): The finite element method with Lagrangian multipliers. Numer. Math., 20, 179–192.zbMATHCrossRefGoogle Scholar
  2. 2.
    Ben Belgacem, F. (1999): The mortar finite element method with Lagrange multipliers. Numer. Math., 84, 173–197.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Bernardi, C., Canute, C., Maday, Y. (1988): Generalized inf-sup conditions for Chebyshev spectral approximation of the Stokes problem. SIAM J. Numer. Anal., 25, 1237–1271.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Bossavit, A. (1998): Computational electromagnetism: variational formulations, complementarity, edge elements. Academic Press, New York.zbMATHGoogle Scholar
  5. 5.
    Brezzi, F., Fortin, M. (1991): Mixed and hybrid finite element methods. Springer, New York.zbMATHCrossRefGoogle Scholar
  6. 6.
    Flemisch, B., Maday, Y., Rapetti, F., Wohlmuth, B.I. (2003): Coupling scalar and vector potentials on nonmatching grids for eddy currents in a moving conductor. To appear in J. Comput. Appl. Math.Google Scholar
  7. 7.
    Flemisch, B., Wohlmuth, B.I. (2003): A domain decomposition method on nested domains and nonmatching grids. To appear in Numer. Methods Partial Differ. Equations.Google Scholar
  8. 8.
    Maday, Y., Rapetti, F., Wohlmuth, B.I. (2003): Mortar element coupling between global scalar and local vector potentials to solve eddy current problems. In: Brezzi, F. et al (eds), Numerical Mathematics and Advanced Applications, Proceedings of ENUMATH 2001, Springer, Berlin, 847–865.CrossRefGoogle Scholar
  9. 9.
    Mair, M., Wohlmuth, B.I. (2003): A domain decomposition method for domains with holes using a complementary decomposition. Report SFB 404 2003/38.Google Scholar
  10. 10.
    Nédélec, J.-C. (1980): Mixed finite elements in IR3. Numer. Math., 35, 315–341.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Nicolaides, R.A. (1982): Existence, uniqueness and approximation for generalized saddle point problems. SIAM J. Numer. Anal., 19, 349–357.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Wahlbin, L.B. (1991): Local behavior in finite element methods. In: Ciarlet, P.C., Lions, J.L. (eds.), Handbook of Numerical Analysis, Vol. II, Elsevier Science Publishers B.V., 1991.Google Scholar
  13. 13.
    Wohlmuth, B.I. (2000): A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J. Numer. Anal., 38, 989–1012.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Bernd Flemisch
    • 1
  • Michael Mair
    • 1
  • Barbara Wohlmuth
    • 1
  1. 1.Inst. for Appl. Analysis and Num. SimulationStuttgartGermany

Personalised recommendations