Numerische Mathematik

, Volume 81, Issue 2, pp 187–209

A posteriori error estimates for mixed FEM in elasticity

  • Carsten Carstensen
  • Georg Dolzmann

DOI: 10.1007/s002110050389

Cite this article as:
Carstensen, C. & Dolzmann, G. Numer. Math. (1998) 81: 187. doi:10.1007/s002110050389

Abstract.

A residue based reliable and efficient error estimator is established for finite element solutions of mixed boundary value problems in linear, planar elasticity. The proof of the reliability of the estimator is based on Helmholtz type decompositions of the error in the stress variable and a duality argument for the error in the displacements. The efficiency follows from inverse estimates. The constants in both estimates are independent of the Lamé constant \(\lambda\), and so locking phenomena for \(\lambda\to\infty\) are properly indicated. The analysis justifies a new adaptive algorithm for automatic mesh–refinement.

Mathematics Subject Classification (1991): 65N30, 65N15, 73C35

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Carsten Carstensen
    • 1
  • Georg Dolzmann
    • 2
  1. 1. Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany; e-mail: cc@numerik.uni-kiel.de DE
  2. 2. Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany; e-mail: georg@mis.mpg.de DE