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

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2006)

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

Abstract

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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.

How to cite

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Barrios, 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. [10] G.N. Gatica, Analysis of a new augmented mixed finite element method for linear elasticity allowing ℝ𝕋 0 - ℙ 1 - ℙ 0 approximations. ESAIM: M2AN 40 (2006) 1–28. Zbl1330.74155
  11. [11] A. Masud and T.J.R. Hughes, A stabilized mixed finite element method for Darcy flow. Comput. Method. Appl. M. 191 (2002) 4341–4370. Zbl1015.76047
  12. [12] J.E. Roberts and J.-M. Thomas, Mixed and Hybrid Methods, in Handbook of Numerical Analysis II, Finite Element Methods (Part 1) P.G. Ciarlet and J.L. Lions Eds., North-Holland, Amsterdam (1991). Zbl0875.65090MR1115239
  13. [13] R. Verfürth, A posteriori error estimation and adaptive mesh-refinement techniques. J. Comput. Appl. Math. 50 (1994) 67–83. Zbl0811.65089
  14. [14] R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner (Chichester) (1996). Zbl0853.65108

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