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Strict error bounds for linear and nonlinear solid mechanics problems using a patch-based flux-free method

Published online by Cambridge University Press:  20 December 2010

Régis Cottereau ,
Ludovic Chamoin  and
Pedro Díez
Régis Cottereau*
Affiliation:
Laboratoire MSSMat, École Centrale Paris, CNRS, Grande voie des vignes, 92295 Châtenay-Malabry, France
Ludovic Chamoin
Affiliation:
LMT-Cachan, ENS Cachan, CNRS, Paris 6 University, 61 avenue du Président Wilson, 94230 Cachan, France
Pedro Díez
Affiliation:
Laboratori de Càlcul Numèric, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain
*
a Corresponding author: pedro.diez@upc.edu
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Abstract

We discuss, in this paper, a common flux-free method for the computation of strict error bounds for linear and nonlinear finite-element computations. In the linear case, the error bounds are on the energy norm of the error, while, in the nonlinear case, the concept of error in constitutive relation is used. In both cases, the error bounds are strict in the sense that they refer to the exact solution of the continuous equations, rather than to some FE computation over a refined mesh. For both linear and nonlinear solid mechanics, this method is based on the computation of a statically admissible stress field, which is performed as a series of local problems on patches of elements. There is no requirement to solve a previous problem of flux equilibration globally, as happens with other methods.

Keywords

Verificationa posteriori error estimationerror boundsresidual-based estimatorsflux-free error estimator
Type
Research Article
Information
Mechanics & Industry , Volume 11 , Issue 3-4: Giens 2009 , May 2010 , pp. 249 - 254
Copyright
© AFM, EDP Sciences 2010

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