Advertisement

Numerische Mathematik

, Volume 99, Issue 1, pp 131–140 | Cite as

On the stability of BDMS and PEERS elements

  • Marco Lonsing
  • Rüdiger VerfürthEmail author
Article

Summary.

Using “Fortin operators” we give a new proof of stability for Stenberg’s family of BDMS elements in linear elasticity. Our approach yields the inf-sup condition with respect to the standard norms, which is indispensable for a posteriori error analysis. Furthermore our technique allows the construction of another family of finite elements strongly related to the classical PEERS element. The given estimates are robust for nearly incompressible materials.

Keywords

Mathematical Method Error Analysis Linear Elasticity Posteriori Error Standard Norm 
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.
    Arnold, D., Brezzi, F., Jun, J.D.: PEERS: A new mixed finite element for plane elasticity. Japan J. Appl. Math. 1, 347–367 (1984)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Arnold, D., Falk, R.: Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Arch. Ration. Mech. Anal. 98, 143–190 (1987)CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Brezzi, F., Fortin, M.: Mixed and hybrid finite element methods. Springer-Verlag, Berlin - Heidelberg - New York, 1991Google Scholar
  4. 4.
    Lonsing, M.: A posteriori Fehlerschätzer für gemischte Finite Elemente in der linearen Elastizität, PhD thesis, Ruhr-Universität Bochum, Fakultät für Mathematik, 2002, http://www.ruhr-uni-bochum.de/num1/arbeiten/diss_lonsing.pdf
  5. 5.
    Lonsing, M., Verfürth, R.: A posteriori error estimators for mixed finite element methods in linear elasticity. Numer. Math. 97, 757–778 (2004)CrossRefGoogle Scholar
  6. 6.
    Stenberg, R.: A family of mixed finite elements for the elasticity problem. Numer. Math. 53, 513–538 (1988)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Ruhr-Universität BochumFakultät für MathematikBochumGermany

Personalised recommendations