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A residual based A POSTERIORI error estimator for an augmented mixed finite element method in linear elasticity

Published online by Cambridge University Press:  16 January 2007

Tomás P. Barrios ,
Gabriel N. Gatica ,
María González  and
Norbert Heuer
Tomás P. Barrios
Affiliation:
Facultad de Ingeniería, Universidad Católica de la Santísima Concepción, Casilla 297, Concepción, Chile.
Gabriel N. Gatica
Affiliation:
GIMA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
María González
Affiliation:
Departamento de Matemáticas, Universidade da Coruña, Campus de Elviña s/n, 15071 A Coruña, Spain.
Norbert Heuer
Affiliation:
BICOM and Department of Mathematical Sciences, Brunel University, Uxbridge, UB8 3PH, UK.
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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.

Keywords

Mixed finite elementaugmented formulationa posteriori error estimatorlinear elasticity.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 5 , September 2006 , pp. 843 - 869
Copyright
© EDP Sciences, SMAI, 2007

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References

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