Numerische Mathematik

, Volume 81, Issue 2, pp 187-209

First online:

A posteriori error estimates for mixed FEM in elasticity

  • Carsten CarstensenAffiliated with Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany; e-mail:
  • , Georg DolzmannAffiliated with Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany; e-mail:

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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