Skip to main content

Part of the book series: NATO ASI Series ((ASIC,volume 384))

Abstract

The paper reviews recent results concerning the mortar element method, which allows for coupling variational discretizations of different types on nonoverlapping subdomains. The basic ideas and proofs are recalled on a model problem, and new extensions are presented.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anagnostou, G. (1991) ‘Nonconforming sliding spectral element methods for the unsteady incompressible Navier-Stokes equations’, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge.

    Google Scholar 

  2. Anagnostou, G., Maday, Y., Mavriplis, C, and Patera, A. T. (1990) ‘On the mortar element method: Generalizations and implementation’, in R. Glowinski (ed.), Third International Conference on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia.

    Google Scholar 

  3. Anagnostou, G., Maday, Y., and Patera, A. T. (1992) ‘A sliding mesh method for partial differential equations in nonstationary geometries: Application to the incompressible Navier-Stokes equations’, SIAM J. Numer. Anal., to appear.

    Google Scholar 

  4. Belhachmi, Z. (1992) Thesis, Université Pierre et Marie Curie, Paris, in preparation.

    Google Scholar 

  5. Ben Belgacem, F. (1992) Thesis, Université Pierre et Marie Curie, Paris, in preparation.

    Google Scholar 

  6. Ben Belgacem, F., and Maday, Y. (1992) ‘Adaptation de la méthode des elements avec joints au couplage spectral-éléments finis, étude de l’erreur pour l’équation de Poisson’, Internai Report Électricité de France.

    Google Scholar 

  7. Ben Belgacem, F., and Maday, Y. (1992) ‘Extension of the mortar element method to three-dimensional domains: Spectral discretization’, in preparation.

    Google Scholar 

  8. Ben Younes, M. (1992) Thesis, Université Pierre et Marie Curie, Paris, in preparation.

    Google Scholar 

  9. Bernardi, C, Dauge, M., and Maday, Y. (1992) ‘Relèvement de traces préservant les polynômes’, Note aux C.R.A.S. Paris, to appear.

    Google Scholar 

  10. Bernardi, C., Debit, N., and Maday, Y. (1987) ‘Couplage de méthodes spectrale et d’éléments finis: premiers résultats d’approximation’, Note aux C.R.A.S. Série I 305, 353–356.

    MathSciNet  MATH  Google Scholar 

  11. Bernardi, C., Debit, N., and Maday, Y. (1990) ‘Coupling finite elements and spectral methods: First results’, Math. Comput. 54, 21–39.

    Article  MathSciNet  Google Scholar 

  12. Bernardi, C., Maday, Y., Mavriplis, C., and Patera, A. T. (1989) ‘The mortar element method applied to spectral discretizations’, in T. J. Chung an G. R. Karr (eds.), Finite Element Analysis in Fluids, Seventh International Conference on Finite Element Methods in Flow Problems, UAH Press, Huntsville.

    Google Scholar 

  13. Bernardi, C., Maday, Y., and Patera, A. T. (1992) ‘A new nonconforming approach to domain decomposition: The mortar element method’, in H. Brézis and J.-L. Lions (eds.), Nonlinear Partial Differential Equations and Their Applications, Collège de France Seminar XI.

    Google Scholar 

  14. Bernardi, C., Maday, Y., and Sacchi-Landriani, G. (1989–90) ‘Nonconforming matching conditions for coupling spectral and finite element methods’, Applied Numer. Math. 6, 65–84.

    Article  MathSciNet  MATH  Google Scholar 

  15. Bjørstad, P. E., and Widlund, O. B. (1986) ‘Iterative methods for the solution of elliptic problems on regions partitioned into substructures’, SIAM J. Numer. Anal. 23, 1097–1120.

    Article  MathSciNet  Google Scholar 

  16. Boland, J., and Nicolaides, R. (1983) ‘Stability of finite elements under divergence constraints’, SIAM J. Numer. Anal. 20, 722–731.

    Article  MathSciNet  MATH  Google Scholar 

  17. Debit, N. (1991) ‘La méthode des éléments avec joints dans le cas du couplage de méthodes spectrales et méthodes d’éléments finis: Résolution des équations de Navier-Stokes, Thesis, Université Pierre et Marie Curie, Paris.

    Google Scholar 

  18. Debit, N., and Maday, Y. (1992) ‘The coupling of spectral and finite element method for the approximation of the Stokes problem’, preprint.

    Google Scholar 

  19. Fisher, P. F., and Patera, A. T. (1991) ‘Parallel spectral element solution of the Stokes problem’, J. Comp. Physics 92, 380–421.

    Article  Google Scholar 

  20. LeTallec, P., and Sassi, T. (1992) ‘The domain decomposition with nonmatching grids’, SIAM J. Numer. Anal., to appear.

    Google Scholar 

  21. Maday, Y., Mavriplis, C., and Patera, A. T. (1988) ‘Nonconforming mortar element methods: Application to spectral discretizations” in T. Chan, R. Glowinski, J. Périaux. and O. B. Widlund (eds.), Second International Conference on Domain Decomposition

    Google Scholar 

  22. Methods for Partial Differential Equations, SIAM, Philadelphia.

    Google Scholar 

  23. Pironneau, O. (1992) Personal communication.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Bernardi, C., Maday, Y., Patera, A.T. (1993). Domain Decomposition by the Mortar Element Method. In: Kaper, H.G., Garbey, M., Pieper, G.W. (eds) Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters. NATO ASI Series, vol 384. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1810-1_17

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-1810-1_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4798-2

  • Online ISBN: 978-94-011-1810-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics