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A posteriori error estimation for the dual mixed finite element method of the elasticity problem in a polygonal domain
Author(s) -
Boulaajine L.,
Farhloul M.,
Paquet L.
Publication year - 2005
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20069
Subject(s) - estimator , mathematics , finite element method , domain decomposition methods , elasticity (physics) , residual , helmholtz equation , helmholtz free energy , a priori and a posteriori , inverse problem , mathematical analysis , mathematical optimization , algorithm , boundary value problem , statistics , philosophy , physics , materials science , epistemology , quantum mechanics , composite material , thermodynamics
In this article, we propose a residual based reliable and efficient error estimator for the new dual mixed finite element method of the elasticity problem in a polygonal domain, introduced by M. Farhloul and M. Fortin. With the help of a specific generalized Helmholtz decomposition of the error on the strain tensor and the classical decomposition of the error on the gradient of the displacements, we show that our global error estimator is reliable. Efficiency of our estimator follows by using classical inverse estimates. The lower and upper error bounds obtained are uniform with respect to the Lamé coefficient λ, in particular avoiding locking phenomena. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005.