Mécanique & Industries
Volume 11, Number 3-4, Mai-Août 2010Giens 2009
|Page(s)||249 - 254|
|Published online||20 December 2010|
Strict error bounds for linear and nonlinear solid mechanics problems using a patch-based flux-free method
Laboratoire MSSMat, École Centrale Paris, CNRS,
Grande voie des
2 LMT-Cachan, ENS Cachan, CNRS, Paris 6 University, 61 avenue du Président Wilson, 94230 Cachan, France
3 Laboratori de Càlcul Numèric, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain
a Corresponding author:
Accepted: 12 July 2010
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.
Key words: Verification / a posteriori error estimation / error bounds / residual-based estimators / flux-free error estimator
© AFM, EDP Sciences 2010
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