A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 5, p. 843-869

In this paper we develop a residual based a posteriori error analysis for an augmented mixed finite element method applied to the problem of linear elasticity in the plane. More precisely, we derive a reliable and efficient a posteriori error estimator for the case of pure Dirichlet boundary conditions. In addition, several numerical experiments confirming the theoretical properties of the estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities and the large stress regions of the solution, are also reported.

DOI : https://doi.org/10.1051/m2an:2006036
Classification:  65N15,  65N30,  65N50,  74B05
Keywords: mixed finite element, augmented formulation, a posteriori error estimator, linear elasticity
@article{M2AN_2006__40_5_843_0,
     author = {Barrios, Tom\'as P. and Gatica, Gabriel N. and Gonz\'alez, Mar\'\i a and Heuer, Norbert},
     title = {A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {5},
     year = {2006},
     pages = {843-869},
     doi = {10.1051/m2an:2006036},
     zbl = {1109.74047},
     mrnumber = {2293249},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2006__40_5_843_0}
}
Barrios, Tomás P.; Gatica, Gabriel N.; González, María; Heuer, Norbert. A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 5, pp. 843-869. doi : 10.1051/m2an:2006036. http://www.numdam.org/item/M2AN_2006__40_5_843_0/

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