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 (2007)

  • 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 40.5 (2007): 843-869. <http://eudml.org/doc/194338>.

@article{Barrios2007,
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},
keywords = {Mixed finite element; augmented formulation; a posteriori error estimator; linear elasticity.; well-posedness; Clément interpolant; localization technique},
language = {eng},
month = {1},
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/194338},
volume = {40},
year = {2007},
}

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
DA - 2007/1//
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/194338
ER -

References

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  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: M2AN40 (2006) 1–28.  
  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.  
  12. J.E. Roberts and J.-M. Thomas, Mixed and Hybrid Methods, in Handbook of Numerical AnalysisII, Finite Element Methods (Part 1) P.G. Ciarlet and J.L. Lions Eds., North-Holland, Amsterdam (1991).  
  13. R. Verfürth, A posteriori error estimation and adaptive mesh-refinement techniques. J. Comput. Appl. Math.50 (1994) 67–83.  
  14. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner (Chichester) (1996).  

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