Skip to main content
SpringerLink
Log in

Non-Conforming Finite Element Methods for Nonmatching Grids in Three Dimensions

  • Conference paper
Domain Decomposition Methods in Science and Engineering

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 40))

Summary

In the last decade, non-conforming domain decomposition methods such as the mortar finite element method have been shown to be reliable techniques for several engineering applications that often employ complex finite element design. With this technique, one can conveniently assemble local subcomponents into a global domain without matching the finite element nodes of each subcomponent at the common interface. In this work, we present computational results for the convergence of a mortar finite element technique in three dimensions for a model problem. We employ the mortar finite element formulation in conjunction with higher-order elements, where both mesh refinement and degree enhancement are combined to increase accuracy. Our numerical results demonstrate optimality for the resulting non-conforming method for various discretizations.

This work of this author is supported in part by the National Science Foundation under Grant DMS 0207327.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  • F. B. Belgacem. The mortar finite element method with lagrange multipliers. Numer. Math., 84:173–197, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  • F. B. Belgacem, L. Chilton, and P. Seshaiyer. The hp-mortar finite-element method for mixed elasticity and stokes problems. Comp. Math. Appl., 46:35–56, 2003.

    Article  Google Scholar 

  • F. B. Belgacem and Y. Maday. The mortar element method for three dimensional finite elements. RAIRO Math. Mod. Numer. Anal., 31:289–302, 1997.

    Google Scholar 

  • F. B. Belgacem, P. Seshaiyer, and M. Suri. Optimal convergence rates of hp mortar finite element methods for second-order elliptic problems. RAIRO Math. Mod. Numer. Anal., 34:591–608, 2000.

    Article  Google Scholar 

  • C. Bernardi, Y. Maday, and A. Patera. Domain decomposition by the mortar finite element method. Asymptotic and Numerical Methods for PDEs with Critical Parameters, 384:269–286, 1993.

    MathSciNet  Google Scholar 

  • D. Braess and W. Dahmen. Stability estimates of the mortar finite element method for 3dimensional problems. East West J. Numer. Math., 6:249–263, 1998.

    MathSciNet  Google Scholar 

  • D. Braess, M. Dryja, and W. Hackbusch. Multigrid method for nonconforming finite element discretization with application to non-matching grids. Comput., 63:1–25, 1999.

    Article  MathSciNet  Google Scholar 

  • W. D. D. Braess and C. Wieners. A multigrid algorithm for the mortar finite element method. SIAM J. Numer. Anal., 37:48–69, 2000.

    Article  MathSciNet  Google Scholar 

  • R. Ewing, R. Lazarov, T. Lin, and Y. Lin. Mortar finite volume element methods of second order elliptic problems. East-West J. Numer. Math., 8:93–110, 2000.

    MathSciNet  Google Scholar 

  • R. E. Ewing and R. D. Lazarov. Superconvergence of the mixed finite element approximations of parabolic problems using rectangular finite elements. East-West J. Numer. Math., 1:199–212, 1993.

    MathSciNet  Google Scholar 

  • C. Kim, R. Lazarov, J. Pasciak, and P. Vassilevski. Multiplier spaces for the mortar finite element method in three dimensions. SIAM J. Numer. Anal., 39:519–538, 2001.

    Article  MathSciNet  Google Scholar 

  • P. Seshaiyer. Stability and convergence of nonconforming hp finite-element methods. Comp. Math. Appl., 46:165–182, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  • P. Seshaiyer and M. Suri. Convergence results for non-conforming hp methods. Contemp. Math., 218:453–459, 1998.

    MathSciNet  Google Scholar 

  • P. Seshaiyer and M. Suri. hp submeshing via non-conforming finite element methods. Comp. Meth. Appl. Mech. Engrg., 189:1011–1030, 2000a.

    Article  MathSciNet  Google Scholar 

  • P. Seshaiyer and M. Suri. Uniform hp convergence results for the mortar finite element method. Math. Comp., 69:521–546, 2000b.

    Article  MathSciNet  Google Scholar 

  • B. I. Wohlmuth. A mortar finite elment method using dual spaces for the lagrange multiplier. SIAM J. Numer. Anal., 38:989–1012, 2000.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics and Statistics, Texas Tech University, Texas

    Wayne McGee & Padmanabhan Seshaiyer

Authors
  1. Wayne McGee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Padmanabhan Seshaiyer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Moffett Field, CA

    Timothy J. Barth

  2. Bonn

    Michael Griebel

  3. New York

    David E. Keyes  & Tamar Schlick  & 

  4. Espoo

    Risto M. Nieminen

  5. Leuven

    Dirk Roose

  6. Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 2-6, 14195, Berlin, Germany

    Ralf Kornhuber

  7. Department of Mathematics, University of Houston, Philip G. Hoffman Hall 651, 77204-3008, Houston, TX, USA

    Ronald Hoppe

  8. Dassault Aviation, 78 Quai Marcel Dassault Cedex 300, 92552, St. Cloud, France

    Jacques Périaux

  9. Laboratoire Jacques-Louis Lions, Université Paris VI, 175 Rue de Chevaleret, 75013, Paris, France

    Olivier Pironneau

  10. Courant Institute of Mathematical Science, New York University, Mercer Street 251, 10012, New York, USA

    Olof Widlund

  11. Department of Mathematics Eberly College of Science, Pennsylvania Sate University, McAllister Building 218, 16802, University Park, PA, USA

    Jinchao Xu

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

McGee, W., Seshaiyer, P. (2005). Non-Conforming Finite Element Methods for Nonmatching Grids in Three Dimensions. In: Barth, T.J., et al. Domain Decomposition Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26825-1_32

Download citation

Publish with us

Policies and ethics

Search

Navigation