# A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity

Tomás P. Barrios; Gabriel N. Gatica; María González; Norbert Heuer

- Volume: 40, Issue: 5, page 843-869
- ISSN: 0764-583X

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topBarrios, Tomás P., et al. "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 40.5 (2006): 843-869. <http://eudml.org/doc/245396>.

@article{Barrios2006,

abstract = {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.},

author = {Barrios, Tomás P., Gatica, Gabriel N., González, María, Heuer, Norbert},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {mixed finite element; augmented formulation; a posteriori error estimator; linear elasticity; well-posedness; Clément interpolant; localization technique},

language = {eng},

number = {5},

pages = {843-869},

publisher = {EDP-Sciences},

title = {A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity},

url = {http://eudml.org/doc/245396},

volume = {40},

year = {2006},

}

TY - JOUR

AU - Barrios, Tomás P.

AU - Gatica, Gabriel N.

AU - González, María

AU - Heuer, Norbert

TI - A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2006

PB - EDP-Sciences

VL - 40

IS - 5

SP - 843

EP - 869

AB - 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.

LA - eng

KW - mixed finite element; augmented formulation; a posteriori error estimator; linear elasticity; well-posedness; Clément interpolant; localization technique

UR - http://eudml.org/doc/245396

ER -

## References

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- [10] G.N. Gatica, Analysis of a new augmented mixed finite element method for linear elasticity allowing ${\mathrm{\mathbb{R}\mathbb{T}}}_{0}-{\mathbb{P}}_{1}-{\mathbb{P}}_{0}$ approximations. ESAIM: M2AN 40 (2006) 1–28. Zbl1330.74155
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