Skip to main content

Nonconforming Discretization Techniques for Overlapping Domain Decompositions

  • Conference paper
Numerical Mathematics and Advanced Applications

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.

Supported in part by DFG, SFB 404, C12.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Babuška, I. (1973): The finite element method with Lagrangian multipliers. Numer. Math., 20, 179–192.

    Article  MATH  Google Scholar 

  2. Ben Belgacem, F. (1999): The mortar finite element method with Lagrange multipliers. Numer. Math., 84, 173–197.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  4. Bossavit, A. (1998): Computational electromagnetism: variational formulations, complementarity, edge elements. Academic Press, New York.

    MATH  Google Scholar 

  5. Brezzi, F., Fortin, M. (1991): Mixed and hybrid finite element methods. Springer, New York.

    Book  MATH  Google Scholar 

  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. 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. 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.

    Chapter  Google Scholar 

  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. Nédélec, J.-C. (1980): Mixed finite elements in IR3. Numer. Math., 35, 315–341.

    Article  MathSciNet  MATH  Google Scholar 

  11. Nicolaides, R.A. (1982): Existence, uniqueness and approximation for generalized saddle point problems. SIAM J. Numer. Anal., 19, 349–357.

    Article  MathSciNet  MATH  Google Scholar 

  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. Wohlmuth, B.I. (2000): A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J. Numer. Anal., 38, 989–1012.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Flemisch, B., Mair, M., Wohlmuth, B. (2004). Nonconforming Discretization Techniques for Overlapping Domain Decompositions. In: Feistauer, M., Dolejší, V., Knobloch, P., Najzar, K. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18775-9_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-18775-9_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62288-5

  • Online ISBN: 978-3-642-18775-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics