Summary.
Three a posteriori error estimators for PEERS and BDMS elements in linear elasticity are presented: one residual error estimator and two estimators based on the solution of auxiliary local problems with different boundary conditions. All of them are reliable and efficient with respect to the standard norm and furthermore robust for nearly incompressible materials.
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Alonso, A.: Error estimators for a mixed method. Numer. Math. 74, 385–395 (1996)
Arnold, D., Brezzi, F., Douglas jun, J.: PEERS: A new mixed finite element for plane elasticity. Japan J. Appl. Math. 1, 347–367 (1984)
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)
Bank, R., Weiser, A.: Some a posteriori error estimators for elliptic partial differential equations. Math. Comput. 44, 283–301 (1985)
Braess, D., Verfürth, R.: A posteriori error estimators for the Raviart-Thomas element. SIAM J. Numer. Anal. 33, 2431–2444 (1996)
Brezzi, F., Fortin, M.: Mixed and hybrid finite element methods. Springer-Verlag, Berlin-Heidelberg-New York, 1991
Carstensen, C.: A posteriori error estimate for the mixed finite element method. Math. Comput. 66, 465–476 (1997)
Carstensen, C., Dolzmann, G.: A posteriori error estimates for mixed fem in elasticity. Numer. Math. 81, 187–209 (1998)
Clément, P.: Approximation by finite element functions using local regularization. RAIRO Anal. Numer. 9, 77–84 (1975)
Girault, V., Raviart, P.: Finite Element Methods for Navier-Stokes Equations. Springer Verlag, Berlin-Heidelberg-New York, 1986
Lonsing, M.: A posteriori Fehlerschätzer für gemischte Finite Elemente in der linearen Elastizität. PhD thesis, Ruhr-Universität Bochum, Fakultät für Math- ematik, 2002 http://www.ruhr-uni-bochum.de/num1/arbeiten/disslonsing.pdf
Lonsing, M., Verfürth, R.: On the stability of BDMS and PEERS elements. Report, Ruhr-Universität Bochum, 2002
Stenberg, R.: A family of mixed finite elements for the elasticity problem. Numer. Math. 53, 513–538 (1988)
Verfürth, R.: A review of a posteriori error estimation and adaptive mesh-refinement techniques. Wiley-Teubner, Chichester-Stuttgart, 1996
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Correspondence to: R. Verfürth
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Lonsing, M., Verfürth, R. A posteriori error estimators for mixed finite element methods in linear elasticity. Numer. Math. 97, 757–778 (2004). https://doi.org/10.1007/s00211-004-0519-8
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DOI: https://doi.org/10.1007/s00211-004-0519-8